Tüm alıştırma soruları

512 soru

Soru 41Soru →

A reconnaissance drone squadron currently takes 14 hours14\text{ hours} to completely map a designated tactical sector when using 66 identical drones simultaneously. If the task force commander requires the exact same sector to be mapped in 4 hours4\text{ hours}, how many total drones must be deployed?

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Cevap: 21

Cevap

2121 drones
The scenario describes an inverse proportion because increasing the number of active drones decreases the time required to finish the mapping. The total mapping workload is a constant 8484 drone-hours (6 drones×14 hours6\text{ drones} \times 14\text{ hours}). To complete this exact same workload in a compressed timeframe of 44 hours, a total of 2121 drones are needed (84÷484 \div 4).

Adım Adım Çözüm

1
Identify the relationship between the variables.
The number of drones and the time required are inversely proportional.
Completing a fixed amount of work faster requires proportionally more equipment.
2
Calculate the total amount of work required (the constant of variation).
6 drones×14 hours=84 drone-hours6\text{ drones} \times 14\text{ hours} = 84\text{ drone-hours}
In an inverse proportion (x×y=kx \times y = k), the product of the two variables remains constant.
3
Calculate the new number of drones required for the target time.
84 drone-hours÷4 hours=21 drones84\text{ drone-hours} \div 4\text{ hours} = 21\text{ drones}
Divide the total work constant by the new required time to solve for the missing variable.

Anahtar Kavram

Inverse proportions occur when one variable increases while another decreases such that their product remains constant (x1×y1=x2×y2x_1 \times y_1 = x_2 \times y_2).
Soru 42Soru →

A quartermaster unit has a bulk roll of heavy-duty canvas measuring 711471 \frac{1}{4} yards in length. The unit needs to manufacture custom protective covers for equipment, with each cover requiring exactly 3343 \frac{3}{4} yards of canvas. How many complete protective covers can the unit manufacture from this roll?

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Cevap: 19

Cevap

19
To find how many items of a specific size can be made from a total amount, you divide the total amount by the size of one item. After converting the mixed numbers to improper fractions (7114=285471 \frac{1}{4} = \frac{285}{4} and 334=1543 \frac{3}{4} = \frac{15}{4}), you multiply 2854\frac{285}{4} by the reciprocal 415\frac{4}{15}. The denominators and numerators simplify to yield exactly 19.

Adım Adım Çözüm

1
Determine the required mathematical operation.
Division: Total canvas length ÷ Length per cover.
You are distributing a total quantity into equal-sized portions.
2
Convert the mixed numbers into improper fractions.
7114=285471 \frac{1}{4} = \frac{285}{4} and 334=1543 \frac{3}{4} = \frac{15}{4}.
Fraction multiplication and division require working with proper or improper fractions rather than mixed numbers.
3
Multiply the first fraction by the reciprocal of the second fraction.
2854×415\frac{285}{4} \times \frac{4}{15}.
Dividing by a fraction is mathematically equivalent to multiplying by its reciprocal.
4
Simplify the expression and calculate the final quotient.
The 4s cancel, leaving 28515=19\frac{285}{15} = 19.
Cross-simplifying makes the calculation much more manageable without needing a calculator.

Anahtar Kavram

Dividing mixed numbers in applied word problems
Soru 43Soru →

A homeowner finances a new refrigerator using a $1,200\$1,200 store credit plan. The plan charges an annual simple interest rate of 5%5\%. If the homeowner pays off the balance in exactly 22 years without any prior payments, what is the total amount of interest paid, in dollars?

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Cevap: 120

Cevap

120
The total interest is found by multiplying the principal amount by the annual interest rate and the time in years. Using the formula I=P×R×TI = P \times R \times T, the calculation is 1200×0.05×21200 \times 0.05 \times 2, which equals $120.

Adım Adım Çözüm

1
Identify the given values for principal, rate, and time.
Principal P=1200P = 1200, Rate R=5%=0.05R = 5\% = 0.05, Time T=2T = 2 years.
These are the necessary variables for the simple interest formula.
2
Apply the simple interest formula.
I=1200×0.05×2I = 1200 \times 0.05 \times 2
The formula for simple interest is I=P×R×TI = P \times R \times T.
3
Calculate the final product.
I=120I = 120
Multiplying the values determines the total interest paid over the 22-year period.

Anahtar Kavram

Calculating simple interest using the formula I=P×R×TI = P \times R \times T
Soru 44Soru →

A restaurant manager wants to purchase a commercial refrigerator with a list price of $3,200\$3,200. Supplier A offers a single discount of 38%38\% off the list price. Supplier B offers a 25%25\% discount off the list price, followed by an additional 15%15\% discount applied to the newly reduced price.

How many dollars does the manager save by choosing the supplier with the lower final price instead of the other supplier?

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Cevap: 56

Cevap

56
Supplier A's final price is $1,984\$1,984 (after a 38%38\% reduction from $3,200\$3,200). Supplier B's final price is $2,040\$2,040 (after a 25%25\% reduction to $2,400\$2,400, followed by a 15%15\% reduction). Choosing Supplier A over Supplier B saves the manager $2,040−$1,984=$56\$2,040 - \$1,984 = \$56.

Adım Adım Çözüm

1
Calculate Supplier A's final sale price.
$1,984\$1,984
Supplier A offers a single 38%38\% discount. 100%−38%=62%100\% - 38\% = 62\%. 0.62×$3,200=$1,9840.62 \times \$3,200 = \$1,984.
2
Calculate Supplier B's price after the initial discount.
$2,400\$2,400
Supplier B offers an initial 25%25\% discount. 100%−25%=75%100\% - 25\% = 75\%. 0.75×$3,200=$2,4000.75 \times \$3,200 = \$2,400.
3
Calculate Supplier B's final sale price.
$2,040\$2,040
Supplier B offers an additional 15%15\% off the reduced price. 100%−15%=85%100\% - 15\% = 85\%. 0.85×$2,400=$2,0400.85 \times \$2,400 = \$2,040.
4
Find the difference between the two final prices.
$56\$56
Subtracting Supplier A's price from Supplier B's price gives the total savings: $2,040−$1,984=$56\$2,040 - \$1,984 = \$56.

Anahtar Kavram

Calculating successive discounts and comparing final sale prices.
Soru 45Soru →

A supply clerk notes that 720\frac{7}{20} of the spare parts inventory needs to be restocked. What decimal represents the portion of the inventory that needs restocking?

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Cevap: 0.35

Cevap

0.35
To convert the fraction 720\frac{7}{20} to a decimal, you divide the numerator (7) by the denominator (20), which equals 0.35. Alternatively, you can multiply both the numerator and denominator by 5 to get the equivalent fraction 35100\frac{35}{100}, which is easily read as the decimal 0.35.

Adım Adım Çözüm

1
Identify the fraction that needs to be converted.
The fraction is 720\frac{7}{20}.
This fraction represents the portion of the inventory to be restocked.
2
Convert the fraction into an equivalent fraction with a base-10 denominator, such as 100.
7×520×5=35100\frac{7 \times 5}{20 \times 5} = \frac{35}{100}
Fractions with a denominator of 100 can be easily and directly written as decimals.
3
Write the resulting fraction as a decimal.
0.35
35100\frac{35}{100} represents 35 hundredths, which is 0.35 in decimal form.

Anahtar Kavram

Converting Fractions to Decimals

Alternatif Yöntem

You can use long division to divide 7.00 by 20. 20 goes into 70 three times (with a remainder of 10). Bring down a 0 to make 100. 20 goes into 100 five times, resulting in 0.35.
Tahmini Süre:45s
Soru 46Soru →

A hobbyist is building a scale model of a historic steam locomotive using a scale of 1:481:48. If the actual locomotive is 60 feet60\text{ feet} long, what is the length of the model locomotive in inches?

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Cevap: 15

Cevap

15
To find the length of the scale model, the actual length of the locomotive must first be converted into inches. Since there are 12 inches12\text{ inches} in a foot, 60 feet60\text{ feet} is equal to 720 inches720\text{ inches}. Using the scale ratio of 1:481:48, divide the actual length in inches by 4848 to find the model's length. Calculating 720÷48720 \div 48 yields a model length of 15 inches15\text{ inches}.

Adım Adım Çözüm

1
Convert the actual length of the locomotive from feet to inches.
60×12=720 inches60 \times 12 = 720\text{ inches}
The question asks for the model length in inches, so it is necessary to match the units before applying the scale factor.
2
Calculate the model length using the 1:481:48 scale ratio.
720÷48=15 inches720 \div 48 = 15\text{ inches}
The scale 1:481:48 means the model is 4848 times smaller than the actual object.

Anahtar Kavram

Applying scale ratios across different units of measurement.
Soru 47Soru →

A warehouse forklift moves 8484 cargo pallets in 66 hours. At this constant rate, how many pallets does the forklift move per hour?

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Cevap: 14

Cevap

The forklift moves 1414 pallets per hour.
To determine the unit rate, divide the total quantity (8484 pallets) by the total elapsed time (66 hours). The result is a constant rate of 1414 pallets per hour.

Adım Adım Çözüm

1
Identify the total quantity of items and the total time.
Total pallets = 8484, Total time = 66 hours.
These are the two values needed to set up the unit rate calculation.
2
Divide the total pallets by the total hours.
84÷6=1484 \div 6 = 14
The unit rate 'pallets per hour' requires dividing the number of pallets by the number of hours.

Anahtar Kavram

Calculating unit rates
Tahmini Süre:45s
Soru 48Soru →

An electronics salesperson earns a base weekly salary of $650\$650 plus a 6%6\% commission on their total sales. If they sell $4,500\$4,500 worth of electronics in one week, what is their total gross pay, in dollars, for that week?

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Cevap: 920

Cevap

920
The total gross pay is the sum of the base salary and the commission earned. The commission is 6%6\% of $4,500\$4,500, which is calculated as 0.06×4500=2700.06 \times 4500 = 270. Adding this to the base salary gives 650+270=920650 + 270 = 920.

Adım Adım Çözüm

1
Calculate the commission earned from sales.
$270\$270
The commission is 6%6\% of the $4,500\$4,500 in total sales. Multiply 45004500 by 0.060.06 to find this amount.
2
Calculate the total gross pay.
$920\$920
Add the commission earned ($270\$270) to the base weekly salary ($650\$650) to determine the total earnings for the week.

Anahtar Kavram

Calculating total gross pay by combining a base salary with a percentage commission.
Soru 49Soru →

A military dining facility prepares 800800 meals for a special event. If 45%45\% of these meals are vegetarian, how many vegetarian meals were prepared?

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Cevap: 360

Cevap

360
To find the number of vegetarian meals, multiply the total number of meals (800800) by the decimal form of the percentage (0.450.45), which yields exactly 360360 meals.

Adım Adım Çözüm

1
Convert the percentage to a decimal.
45%=0.4545\% = 0.45
Percentages must be converted to decimals or fractions to perform arithmetic operations.
2
Multiply the total quantity by the decimal.
800×0.45=360800 \times 0.45 = 360
To find a percentage of a quantity, multiply the total by the decimal equivalent of the percentage.

Anahtar Kavram

Calculating a percentage of a given whole number
Tahmini Süre:45s
Soru 50Soru →

A logistical transport convoy travels along a main supply route at a steady speed of 55 miles per hour55\text{ miles per hour}. If the journey takes exactly 3 hours and 36 minutes3\text{ hours and } 36\text{ minutes}, what is the total distance traveled in miles?

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Cevap: 198

Cevap

The convoy traveled a total distance of 198 miles.
The correct total distance is determined by first converting the mixed travel time entirely into hours (3.6 hours3.6\text{ hours}) and then multiplying it by the constant speed (55 mph55\text{ mph}) to yield exactly 198 miles198\text{ miles}.

Adım Adım Çözüm

1
Convert the travel time into a single unit (hours) to match the rate.
3 hours and 36 minutes=3+3660 hours=3.6 hours3\text{ hours and } 36\text{ minutes} = 3 + \frac{36}{60}\text{ hours} = 3.6\text{ hours}.
The speed is given in miles per hour, so the time must be represented entirely in hours before multiplying.
2
Apply the distance formula: Distance = Rate ×\times Time.
Distance = 55×3.655 \times 3.6
This formula determines the total distance covered over a specific time frame at a constant speed.
3
Calculate the final distance.
198198
Multiplying the constant rate of 55 mph55\text{ mph} by the total duration of 3.6 hours3.6\text{ hours} yields the total miles traveled.

Anahtar Kavram

Calculating distance using a constant rate and converting mixed time units.
Soru 51Soru →

An architect is designing a community center and reviewing the floor plan. The floor plan uses a scale of 34 inch=5 feet\frac{3}{4}\text{ inch} = 5\text{ feet}. If the main hall measures 4.5 inches4.5\text{ inches} long on the floor plan, what is the actual length of the main hall in feet?

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Cevap: 30

Cevap

30
The correct answer is found by setting up a proportion or finding the unit rate. Since 34 inch\frac{3}{4}\text{ inch} represents 5 feet5\text{ feet}, 1 inch1\text{ inch} represents 203 feet\frac{20}{3}\text{ feet}. Multiplying the drawing measurement of 4.5 inches4.5\text{ inches} by 203 feet per inch\frac{20}{3}\text{ feet per inch} yields exactly 30 feet30\text{ feet}.

Adım Adım Çözüm

1
Find the actual distance represented by one inch.
1 inch=5÷34=5×43=203 feet1\text{ inch} = 5 \div \frac{3}{4} = 5 \times \frac{4}{3} = \frac{20}{3}\text{ feet}
Establishing a unit rate simplifies calculating the actual length for any given map measurement.
2
Multiply the unit rate by the blueprint measurement.
4.5×203=92×203=1806=30 feet4.5 \times \frac{20}{3} = \frac{9}{2} \times \frac{20}{3} = \frac{180}{6} = 30\text{ feet}
Multiplying the map length by the actual distance per inch gives the total actual length.

Anahtar Kavram

Solving scale drawing problems using proportions or unit rates.
Soru 52Soru →

A squad of soldiers is conducting a foot march along a trail that is 1212 miles long. If they maintain a steady pace of 33 miles per hour, how many hours will it take them to complete the march?

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Cevap: 4

Cevap

4
Using the fundamental relationship Time=DistanceRate\text{Time} = \frac{\text{Distance}}{\text{Rate}}, we divide the total distance of 1212 miles by the steady pace of 33 miles per hour. This calculation (12÷312 \div 3) results in exactly 44 hours.

Adım Adım Çözüm

1
Identify the given values for the distance and the rate of travel.
Distance = 1212 miles, Rate = 33 miles per hour.
These values are required to calculate the total elapsed time.
2
Apply the appropriate formula to find the time.
Time=DistanceRate\text{Time} = \frac{\text{Distance}}{\text{Rate}}
Time is equal to total distance divided by the speed.
3
Substitute the values and calculate the result.
123=4\frac{12}{3} = 4
Dividing the distance by the rate gives the total time in hours.

Anahtar Kavram

Calculating elapsed time given distance and rate.
Tahmini Süre:45s
Soru 53Soru →

A military mess hall requires exactly 500500 pounds of flour. Supplier A sells flour in 2525-pound bags for $14.00\$14.00 per bag. Supplier B sells the same flour in 4040-ounce boxes for $1.50\$1.50 per box. How much total money, in dollars, is saved by purchasing the entire 500500 pounds from the more cost-effective supplier instead of the less cost-effective one?

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Cevap: 20

Cevap

The savings amount to 20 dollars.
Supplier A's total cost for 500 pounds is 280(20bags×280 (20 bags × 14.00), and Supplier B's total cost is 300(200boxes×300 (200 boxes × 1.50). Purchasing from Supplier A saves $20.

Adım Adım Çözüm

1
Convert the weight of Supplier B's boxes from ounces to pounds.
4040 ounces ÷16\div 16 ounces/pound = 2.52.5 pounds per box.
Measurements must be in the same unit (pounds) to accurately calculate the required number of packages and compare costs.
2
Determine the number of packages required from each supplier to get exactly 500 pounds.
Supplier A: 500÷25=20500 \div 25 = 20 bags. Supplier B: 500÷2.5=200500 \div 2.5 = 200 boxes.
This establishes the exact purchasing volume needed for the final cost calculation.
3
Calculate the total cost for each supplier.
Supplier A: 2020 bags ×$14.00\times \$14.00 = $280\$280. Supplier B: 200200 boxes ×$1.50\times \$1.50 = $300\$300.
Total cost is the package count multiplied by the price per package.
4
Calculate the difference between the two total costs.
$300−$280=$20\$300 - \$280 = \$20.
Subtracting the most cost-effective option from the alternative gives the total savings.

Anahtar Kavram

Calculating and comparing total costs across different measurement units by determining unit prices and required volumes.

Alternatif Yöntem

Instead of computing total costs, calculate the unit price per pound for both. Supplier A: $14.00÷25=$0.56\$14.00 \div 25 = \$0.56 per pound. Supplier B: 4040 oz is 2.52.5 lbs; $1.50÷2.5=$0.60\$1.50 \div 2.5 = \$0.60 per pound. The difference is $0.04\$0.04 per pound. Multiply this difference by the 500500 pounds needed: 500×$0.04=$20500 \times \$0.04 = \$20.
Tahmini Süre:2m 30s
Soru 54Soru →

A mechanic needs to buy a new set of socket wrenches. The regular price of the set is $150.00\$150.00. If the store is offering a 30%30\% discount on all tools, what is the final sale price of the socket wrench set in dollars?

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Cevap: 105

Cevap

The final sale price is $105.00\$105.00.
The correct answer is found by first determining the dollar value of the discount. A 30%30\% discount on $150.00\$150.00 is calculated as 150×0.30150 \times 0.30, which equals $45.00\$45.00. Subtracting this discount from the original price (150−45150 - 45) gives the final sale price of $105.00\$105.00.

Adım Adım Çözüm

1
Calculate the discount amount.
$150.00×0.30=$45.00\$150.00 \times 0.30 = \$45.00
To find out how much money is being taken off the regular price.
2
Subtract the discount amount from the regular price.
$150.00−$45.00=$105.00\$150.00 - \$45.00 = \$105.00
To determine the final sale price after the discount is applied.

Anahtar Kavram

Calculating a single-step discount and determining the final sale price.
Soru 55Soru →

A supply clerk is comparing prices for standard issue notebooks. Vendor A sells a pack of 55 notebooks for 15.0015.00 dollars. Vendor B sells a bulk box of 2020 notebooks for 48.0048.00 dollars. What is the savings per notebook, in dollars, if the clerk chooses Vendor B instead of Vendor A?

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Cevap: 0.6

Cevap

0.60
The unit price is found by dividing the total cost by the quantity. Vendor A charges 15.00÷5=3.0015.00 \div 5 = 3.00 dollars per notebook. Vendor B charges 48.00÷20=2.4048.00 \div 20 = 2.40 dollars per notebook. The savings per notebook is the difference: 3.00−2.40=0.603.00 - 2.40 = 0.60 dollars.

Adım Adım Çözüm

1
Calculate Vendor A's unit price
3.003.00 dollars per notebook
To find the cost of a single item in a package, divide the total price by the number of items (15.00÷515.00 \div 5).
2
Calculate Vendor B's unit price
2.402.40 dollars per notebook
Divide the bulk box total price by the number of notebooks it contains (48.00÷2048.00 \div 20).
3
Calculate the difference between the two unit prices
0.600.60 dollars
Subtracting Vendor B's unit price from Vendor A's unit price (3.00−2.403.00 - 2.40) gives the exact savings per notebook.

Anahtar Kavram

Unit price calculation and comparison
Soru 56Soru →

A logistics unit is transporting a total of 300300 supply crates. If 25%25\% of the crates contain medical equipment, how many medical crates are in the transport?

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Cevap: 75

Cevap

75
By converting 25%25\% to the fraction 14\frac{1}{4} (or the decimal 0.250.25) and multiplying it by the total of 300300 supply crates, we determine that exactly 7575 crates contain medical equipment.

Adım Adım Çözüm

1
Convert the given percentage to a decimal or a simple fraction.
25%=0.2525\% = 0.25 or 14\frac{1}{4}
Percentages must be converted into decimals or fractions before performing calculations with a base quantity.
2
Multiply the total quantity by the converted decimal or fraction to find the portion.
300×0.25=75300 \times 0.25 = 75
Finding a percentage 'of' a number indicates multiplication.

Anahtar Kavram

To calculate a percentage of a quantity, convert the percent to a decimal or fraction and multiply it by the total amount.
Tahmini Süre:45s
Soru 57Soru →

A structural engineer is analyzing a blueprint for a steel bridge truss. The blueprint uses a scale where 78 inch\frac{7}{8}\text{ inch} represents an actual length of 21 feet21\text{ feet}. If a particular support beam measures 6.5 inches6.5\text{ inches} on the blueprint, what is the actual length of this beam in feet?

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Cevap: 156

Cevap

156
The correct answer is found by establishing a proportion based on the scale. Since 78 inch\frac{7}{8}\text{ inch} equals 21 feet21\text{ feet}, 1 inch1\text{ inch} must equal 21÷7821 \div \frac{7}{8}, which is 24 feet24\text{ feet}. Multiplying the blueprint length of 6.5 inches6.5\text{ inches} by this unit rate of 2424 gives an actual length of 156 feet156\text{ feet}.

Adım Adım Çözüm

1
Determine the unit scale factor in feet per inch.
21÷78=24 feet/inch21 \div \frac{7}{8} = 24\text{ feet/inch}
Finding the actual distance represented by a single inch creates a simple multiplier for any dimension on the blueprint.
2
Multiply the measurement on the blueprint by the unit scale factor.
6.5×24=156 feet6.5 \times 24 = 156\text{ feet}
Scaling up the drawing measurement by the unit rate yields the actual real-world length of the beam.

Anahtar Kavram

Direct proportions and unit rates in scale drawings

Alternatif Yöntem

You can set up a direct proportion: 7821=6.5x\frac{\frac{7}{8}}{21} = \frac{6.5}{x}. Cross-multiplying gives 78x=136.5\frac{7}{8}x = 136.5. Multiplying both sides by 87\frac{8}{7} yields x=156x = 156.
Tahmini Süre:1m 0s
Soru 58Soru →

A dispatch rider is transporting urgent documents between two military installations. The rider travels on a paved highway at a constant speed of 65 mph65\text{ mph} for 1 hour and 12 minutes1\text{ hour and } 12\text{ minutes}. Upon reaching a rural sector, the rider continues on an unpaved route at a steady speed of 42 mph42\text{ mph} for 35 minutes35\text{ minutes}. What is the total distance, in miles, the dispatch rider traveled?

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Cevap: 102.5

Cevap

102.5
To find the total distance, calculate the distance for each leg of the trip separately by ensuring time is expressed in hours. For the first leg, 1 hour and 12 minutes1\text{ hour and } 12\text{ minutes} is 1.2 hours1.2\text{ hours}. Multiplying the 65 mph65\text{ mph} rate by 1.2 hours1.2\text{ hours} gives 78 miles78\text{ miles}. For the second leg, 35 minutes35\text{ minutes} is 3560\frac{35}{60} or 712 of an hour\frac{7}{12}\text{ of an hour}. Multiplying the 42 mph42\text{ mph} rate by 712 hours\frac{7}{12}\text{ hours} gives 24.5 miles24.5\text{ miles}. Adding these two distances together (78+24.578 + 24.5) gives a total of 102.5 miles102.5\text{ miles}.

Adım Adım Çözüm

1
Convert the highway travel time into hours.
1 hour and 12 minutes=1+1260 hours=1.2 hours1\text{ hour and } 12\text{ minutes} = 1 + \frac{12}{60}\text{ hours} = 1.2\text{ hours}.
The speed is given in miles per hour, so time must be converted to hours to match units.
2
Calculate the distance traveled on the highway.
65 mph×1.2 hours=78 miles65\text{ mph} \times 1.2\text{ hours} = 78\text{ miles}.
Applying the formula: Distance = Rate ×\times Time.
3
Convert the unpaved route travel time into hours.
35 minutes=3560 hours=712 hours35\text{ minutes} = \frac{35}{60}\text{ hours} = \frac{7}{12}\text{ hours}.
Time must be in hours for consistency with the speed unit.
4
Calculate the distance traveled on the unpaved route.
42 mph×712 hours=24.5 miles42\text{ mph} \times \frac{7}{12}\text{ hours} = 24.5\text{ miles}.
Applying the formula: Distance = Rate ×\times Time.
5
Calculate the total distance.
78 miles+24.5 miles=102.5 miles78\text{ miles} + 24.5\text{ miles} = 102.5\text{ miles}.
The total journey distance is the sum of the individual distances from each leg.

Anahtar Kavram

Calculating total distance for a multi-leg journey by accurately converting fractional times to hours and applying the distance formula.
Soru 59Soru →

A combat engineering detachment is mixing a specialized rapid-setting concrete. The dry mix requires sand, gravel, and cement in a ratio of 4:5:24:5:2 by weight. If the engineers need to prepare exactly 3,3003,300 pounds of the dry mix for a runway repair, how many pounds of gravel are required?

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Cevap: 1500

Cevap

1500
To find the correct amount of gravel, the total weight of 3,3003,300 pounds is divided by the total number of parts in the ratio (4+5+2=114 + 5 + 2 = 11) to find the weight of one part (300300 pounds). The gravel's share is 5 parts, so multiplying 300300 pounds by 5 yields exactly 1,5001,500 pounds.

Adım Adım Çözüm

1
Find the total number of parts in the ratio.
4+5+2=114 + 5 + 2 = 11 total parts
To distribute the total weight proportionally, you first need to know how many equal parts make up the entire mixture.
2
Determine the weight of one single part.
3,300÷11=3003,300 \div 11 = 300 pounds
Dividing the total weight of the mix by the total number of parts gives the value of one part.
3
Calculate the specific weight required for the gravel.
300×5=1,500300 \times 5 = 1,500 pounds
The ratio specifies 5 parts of gravel. Multiplying the weight of one part by 5 gives the total weight of the gravel.

Anahtar Kavram

Dividing a total quantity into given ratio parts.
Soru 60Soru →

An aviation maintenance squadron stocks a specific fastener kit containing standard bolts, lock washers, and retaining nuts in a ratio of 7:4:37:4:3. If a master storage bin contains a total of 840840 of these combined items in this exact ratio, how many lock washers are in the bin?

Cevabı ve açıklamayı göster

Cevap: 240

Cevap

There are 240 lock washers in the bin.
The total number of items (840840) is divided by the sum of all ratio parts (1414) to find the value of a single share (6060). This share is then multiplied by the specific ratio number corresponding to lock washers (44) to find the final quantity (240240).

Adım Adım Çözüm

1
Calculate the total number of parts in the ratio.
7+4+3=147 + 4 + 3 = 14 parts
To determine what fraction of the total bin corresponds to a single proportional unit.
2
Determine the physical number of items represented by one part.
840÷14=60840 \div 14 = 60 items
Dividing the total inventory by the total ratio parts gives the baseline value of a single share.
3
Calculate the specific number of lock washers.
4×60=2404 \times 60 = 240 lock washers
The ratio specifies there are 44 parts of lock washers, and each part equals 6060 items.

Anahtar Kavram

Allocating a total known quantity into specific amounts based on a multi-term part-to-part ratio.
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