Unit Price Comparisons

15 soru

Soru 1Soru →

A base logistics officer needs to requisition 1,500 feet of paracord. Distributor A sells a 100-yard spool of paracord for 36.00.DistributorBsellsthesameparacordina50−footrollfor36.00. Distributor B sells the same paracord in a 50-foot roll for 5.50. If the officer purchases the entire 1,500 feet from the distributor with the lower overall cost, how much total money will be saved compared to purchasing from the more expensive distributor?

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Cevap: $15.00

Cevap

The total savings is $15.00 when purchasing from Distributor B instead of Distributor A.
The correct answer is found by equalizing the units and calculating the total cost required to obtain 1,500 feet from each distributor. Distributor A provides 300 feet (100 yards) per 36.00spool,so5spoolsareneeded,costing36.00 spool, so 5 spools are needed, costing 180.00. Distributor B provides 50 feet per 5.50roll,so30rollsareneeded,costing5.50 roll, so 30 rolls are needed, costing 165.00. The total savings is the difference: 180.00−180.00 - 165.00 = $15.00.

Adım Adım Çözüm

1
Calculate the total cost if buying from Distributor A.
100 yards × 3 feet/yard = 300 feet per spool. Number of spools needed = 1,500 feet ÷ 300 feet/spool = 5 spools. Total cost = 5 × 36.00=36.00 = 180.00.
Units must be consistent (feet) to compare or fulfill the 1,500-foot requirement accurately.
2
Calculate the total cost if buying from Distributor B.
Number of rolls needed = 1,500 feet ÷ 50 feet/roll = 30 rolls. Total cost = 30 × 5.50=5.50 = 165.00.
We must find the exact total cost for fulfilling the entire requisition of 1,500 feet with the second option.
3
Find the difference between the two total costs to determine savings.
180.00−180.00 - 165.00 = $15.00.
Subtracting the lower cost from the higher cost reveals the total amount saved.

Anahtar Kavram

Comparing unit prices across different bulk packages by establishing a common metric or total purchasing cost.
Soru 2Soru →

A motor pool mechanic needs to buy spark plugs. A single spark plug costs 3.00.Aboxofonedozensparkplugscosts3.00. A box of one dozen spark plugs costs 24.00. How much money is saved per spark plug by purchasing the box instead of buying them individually?

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Cevap: $1.00

Cevap

$1.00
Purchasing the box of one dozen means buying 12 spark plugs for 24.00,whichresultsinaunitpriceof24.00, which results in a unit price of 2.00 each (24.00÷12).Buyingthemindividuallycosts24.00 ÷ 12). Buying them individually costs 3.00 each. The difference per spark plug is 3.00−3.00 - 2.00 = $1.00.

Adım Adım Çözüm

1
Determine the total number of items in the box.
1 dozen = 12 spark plugs.
To find the cost of a single spark plug from the box, the total quantity is required.
2
Calculate the unit price of a spark plug from the box.
24.00÷12=24.00 ÷ 12 = 2.00 per spark plug.
Dividing the total cost by the quantity yields the price per individual item.
3
Calculate the savings per spark plug.
3.00−3.00 - 2.00 = $1.00.
Subtracting the bulk unit price from the individual unit price gives the savings per item.

Anahtar Kavram

Unit Price Comparisons
Soru 3Soru →

An armory quartermaster is ordering gun solvent for weapons maintenance. The solvent is available in four different packaging options. Arrange the options from the lowest price per gallon to the highest price per gallon.

Öğeleri doğru sıraya koymak için sürükleyin

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Cevap

The correct order from lowest to highest price per gallon is: 2-quart bottle, 5-gallon bucket, 4-gallon case, 1-pint bottle.
By converting all package volumes into gallons, we can compare their unit prices accurately. The 22-quart bottle costs $12.00\$12.00 per gallon, the 55-gallon bucket costs $13.00\$13.00 per gallon, the 44-gallon case costs $13.50\$13.50 per gallon, and the 11-pint bottle costs $14.00\$14.00 per gallon. Arranging them from lowest to highest yields this sequence.

Adım Adım Çözüm

1
Calculate the unit price for the 22-quart bottle.
$12.00\$12.00 per gallon
There are 44 quarts in a gallon, making 22 quarts equivalent to 0.50.5 gallons. $6.00÷0.5=$12.00\$6.00 \div 0.5 = \$12.00 per gallon.
2
Calculate the unit price for the 55-gallon bucket.
$13.00\$13.00 per gallon
Dividing the total cost by the number of gallons: $65.00÷5=$13.00\$65.00 \div 5 = \$13.00 per gallon.
3
Calculate the unit price for the 44-gallon case.
$13.50\$13.50 per gallon
Dividing the total cost by the number of gallons: $54.00÷4=$13.50\$54.00 \div 4 = \$13.50 per gallon.
4
Calculate the unit price for the 11-pint bottle.
$14.00\$14.00 per gallon
There are 88 pints in a gallon. Multiplying the pint price by 88 gives the gallon price: $1.75×8=$14.00\$1.75 \times 8 = \$14.00 per gallon.
5
Order the unit prices from lowest to highest.
$12.00\$12.00, $13.00\$13.00, $13.50\$13.50, $14.00\$14.00
The question asks for the options to be arranged in ascending order based on their price per gallon.

Anahtar Kavram

Converting various liquid volume measurements to a common unit (gallons) in order to accurately compare unit prices.
Soru 4Soru →

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 5Soru →

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 6Soru →

A cafeteria chef is purchasing black pepper. A 44-ounce jar of black pepper costs $8.00\$8.00. A 11-pound container of the same black pepper costs $16.00\$16.00. How much money is saved per ounce by purchasing the 11-pound container instead of the 44-ounce jar?

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Cevap: \$1.00

Cevap

The correct answer is $1.00\$1.00 saved per ounce.
The unit price of the 44-ounce jar is calculated by dividing its cost by its size: $8.00÷4 ounces=$2.00\$8.00 \div 4 \text{ ounces} = \$2.00 per ounce. Next, convert the 11-pound container to ounces, knowing that 1 pound=16 ounces1 \text{ pound} = 16 \text{ ounces}. The unit price of the 11-pound container is $16.00÷16 ounces=$1.00\$16.00 \div 16 \text{ ounces} = \$1.00 per ounce. The savings per ounce is found by subtracting the lower unit price from the higher unit price: $2.00−$1.00=$1.00\$2.00 - \$1.00 = \$1.00.

Adım Adım Çözüm

1
Calculate the price per ounce for the 44-ounce jar.
$8.00÷4=$2.00\$8.00 \div 4 = \$2.00 per ounce
To compare prices, we need the unit price of the first option.
2
Convert the weight of the 11-pound container into ounces.
$1 \text{ pound} = 16 \text{ ounces}
Unit prices must be in the same measurement unit (ounces) to be compared.
3
Calculate the price per ounce for the 11-pound container.
$16.00÷16=$1.00\$16.00 \div 16 = \$1.00 per ounce
This establishes the unit price of the second option for comparison.
4
Subtract the lower unit price from the higher unit price to find the savings.
$2.00−$1.00=$1.00\$2.00 - \$1.00 = \$1.00 per ounce
The question asks for the exact amount of money saved per ounce.

Anahtar Kavram

Comparing unit prices requires converting different units of measurement into a common unit (like ounces) before dividing cost by quantity.
Tahmini Süre:45s
Soru 7Soru →

A quartermaster is evaluating different vendors to purchase AA batteries. Calculate the price per battery for each option and arrange the vendors in order from the lowest unit price to the highest unit price.

Öğeleri doğru sıraya koymak için sürükleyin

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Cevap

Vendor Delta, Vendor Bravo, Vendor Alpha, Vendor Charlie
The correct sequence is found by evaluating the cost per single battery for each vendor. By dividing the total cost by the quantity provided, we find that Vendor Delta offers the lowest rate at $0.70\$0.70 per battery. Vendor Bravo follows at $0.80\$0.80 per battery, Vendor Alpha at $0.90\$0.90 per battery, and Vendor Charlie is the most expensive at $1.25\$1.25 per battery. Arranging these calculated unit prices from smallest to largest provides the correct order.

Adım Adım Çözüm

1
Calculate the unit price for Vendor Alpha.
$9.00÷10=$0.90\$9.00 \div 10 = \$0.90 per battery.
To find the cost of a single battery, divide the total cost by the quantity.
2
Calculate the unit price for Vendor Bravo.
$9.60÷12=$0.80\$9.60 \div 12 = \$0.80 per battery.
To find the cost of a single battery, divide the total cost by the quantity.
3
Calculate the unit price for Vendor Charlie.
$2.50÷2=$1.25\$2.50 \div 2 = \$1.25 per battery.
To find the cost of a single battery, divide the total cost by the quantity.
4
Calculate the unit price for Vendor Delta.
$21.00÷30=$0.70\$21.00 \div 30 = \$0.70 per battery.
To find the cost of a single battery, divide the total cost by the quantity.
5
Order the calculated unit prices from lowest to highest.
$0.70\$0.70 (Delta) < $0.80\$0.80 (Bravo) < $0.90\$0.90 (Alpha) < $1.25\$1.25 (Charlie)
This establishes the correct sequence from the most cost-effective to the least cost-effective option.

Anahtar Kavram

Unit price is calculated by dividing the total price by the number of units. Comparing these prices reveals the lowest cost per item.
Soru 8Soru →

A base recreation center needs to purchase tennis balls for an upcoming tournament. A single can of tennis balls costs $4.50\$4.50. A case containing 1010 cans costs $40.00\$40.00. How much money is saved per can by purchasing the case instead of individual cans?

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Cevap: $0.50\$0.50

Cevap

$0.50\$0.50
Purchasing the case means each can costs $40.00\$40.00 divided by 1010, which is $4.00\$4.00 per can. Subtracting this bulk unit price from the individual price of $4.50\$4.50 gives a savings of $0.50\$0.50 per can.

Adım Adım Çözüm

1
Calculate the unit price of a single can when bought by the case.
$40.00÷10=$4.00\$40.00 \div 10 = \$4.00 per can
To compare prices on equal terms, you must find the cost of one unit for the bulk option.
2
Calculate the difference between the individual can price and the bulk unit price.
$4.50−$4.00=$0.50\$4.50 - \$4.00 = \$0.50
Subtracting the lower unit price from the higher individual price reveals the exact savings per can.

Anahtar Kavram

Comparing the unit rate of a bulk purchase to an individual item price to determine savings.
Tahmini Süre:45s
Soru 9Soru →

A ship's culinary specialist is ordering bulk ground coffee. A 1212-ounce bag of coffee costs $5.40\$5.40. A 33-pound container of the same coffee costs $18.00\$18.00. How much money is saved per pound by purchasing the 33-pound container instead of multiple 1212-ounce bags?

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Cevap: $1.20\$1.20

Cevap

$1.20\$1.20
The correct savings is found by determining the unit price of each option for exactly one pound and subtracting them. The 1212-ounce bag costs $0.45\$0.45 per ounce, which equates to $7.20\$7.20 per pound (0.45×160.45 \times 16). The 33-pound container costs $6.00\$6.00 per pound (18.00÷318.00 \div 3). Subtracting the container's unit price from the bag's unit price yields a savings of $1.20\$1.20 per pound.

Adım Adım Çözüm

1
Calculate the price per pound for the 33-pound container.
$18.00÷3=$6.00\$18.00 \div 3 = \$6.00 per pound.
To find the baseline unit price of the bulk option for comparison.
2
Determine the cost per ounce of the 1212-ounce bag.
$5.40÷12=$0.45\$5.40 \div 12 = \$0.45 per ounce.
To find the base unit rate of the smaller bags before scaling up to a full pound.
3
Calculate the price per pound for the 1212-ounce bag.
$0.45×16=$7.20\$0.45 \times 16 = \$7.20 per pound.
Because there are 1616 ounces in a pound, multiplying the cost per ounce by 1616 gives the comparable unit price.
4
Find the difference in price per pound.
$7.20−$6.00=$1.20\$7.20 - \$6.00 = \$1.20.
Subtracting the unit price of the bulk container from the unit price of the bags determines the exact savings per pound.

Anahtar Kavram

Unit Price Comparisons across different measurement scales
Tahmini Süre:1m 30s
Soru 10Soru →

An aviation logistics specialist is sourcing a specific synthetic lubricant for aircraft maintenance. A local supplier sells the lubricant in 11-quart bottles for $5.50\$5.50 each. A wholesale distributor sells the same lubricant in 55-gallon drums for $95.00\$95.00 per drum. How much money is saved per gallon by purchasing the 55-gallon drum instead of the individual 11-quart bottles?

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Cevap: 3

Cevap

3
To find the savings per gallon, both purchase options must be converted to a per-gallon rate. Because there are 4 quarts in a US gallon, the 1-quart bottles effectively cost $5.50×4=$22.00\$5.50 \times 4 = \$22.00 per gallon. The 5-gallon drum costs $95.00÷5=$19.00\$95.00 \div 5 = \$19.00 per gallon. The difference in price is $22.00−$19.00=$3.00\$22.00 - \$19.00 = \$3.00 saved per gallon.

Adım Adım Çözüm

1
Calculate the price per gallon for the 1-quart bottles.
$5.50×4=$22.00\$5.50 \times 4 = \$22.00 per gallon.
There are 4 quarts in a gallon, so the unit price must be scaled up to match the gallon comparison unit.
2
Calculate the price per gallon for the 5-gallon drum.
$95.00÷5=$19.00\$95.00 \div 5 = \$19.00 per gallon.
The total cost of the drum must be divided by its volume in gallons to find the unit price.
3
Calculate the difference between the two unit prices.
$22.00−$19.00=$3.00\$22.00 - \$19.00 = \$3.00
Subtracting the lower unit price from the higher unit price reveals the savings per gallon.

Anahtar Kavram

Calculating and comparing unit rates involving US customary capacity conversions.
Soru 11Soru →

A construction battalion is procuring wood varnish for a barracks renovation. A supplier sells the varnish in a 55-gallon bucket for $120.00\$120.00. Alternatively, the same varnish is sold in 11-quart cans for $8.00\$8.00 each. How much money is saved per gallon by purchasing the 55-gallon bucket instead of the 11-quart cans?

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Cevap: \$8.00

Cevap

The 55-gallon bucket saves $8.00\$8.00 per gallon compared to the 11-quart cans.
To accurately compare the costs, both options must be calculated as a price per gallon. The 55-gallon bucket costs $120.00\$120.00, which breaks down to $120.00÷5=$24.00\$120.00 \div 5 = \$24.00 per gallon. For the second option, because there are 44 quarts in 11 gallon, the price per gallon is 4×$8.00=$32.004 \times \$8.00 = \$32.00. The savings per gallon is the difference between these two unit rates: $32.00−$24.00=$8.00\$32.00 - \$24.00 = \$8.00.

Adım Adım Çözüm

1
Calculate the unit price per gallon for the 55-gallon bucket.
$120.00÷5=$24.00\$120.00 \div 5 = \$24.00 per gallon
This establishes the baseline unit price for the bulk option.
2
Convert the price of the 11-quart cans into a price per gallon.
Since there are 44 quarts in a gallon, 4×$8.00=$32.004 \times \$8.00 = \$32.00 per gallon
Both unit prices must be in the same measurement (gallons) to make an accurate comparison.
3
Subtract the bucket's gallon price from the cans' gallon price to find the savings.
$32.00−$24.00=$8.00\$32.00 - \$24.00 = \$8.00
The question asks for the money saved per gallon by choosing the bucket.

Anahtar Kavram

Comparing unit prices requiring unit conversions
Soru 12Soru →

A field medical unit needs to resupply liquid surface disinfectant. The disinfectant is available in four different packaging options. Arrange the purchasing options in order from the lowest unit price (price per gallon) to the highest unit price.

Öğeleri doğru sıraya koymak için sürükleyin

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Cevap

The correct order from lowest to highest unit price is: the pack of eight 1-pint bottles ($23.04\$23.04/gal), the twin-pack of two 1-gallon jugs ($24.00\$24.00/gal), the 5-gallon drum ($25.60\$25.60/gal), and the case of four 1-quart bottles ($28.16\$28.16/gal).
By converting the capacity of each option to a common unit (gallons) and calculating the price per gallon, we can directly compare the unit costs. The 11-pint bottles equate to 11 gallon for $23.04\$23.04. The 11-gallon jugs cost $24.00\$24.00 per gallon ($48.00÷2\$48.00 \div 2). The 55-gallon drum costs $25.60\$25.60 per gallon ($128.00÷5\$128.00 \div 5). The 11-quart bottles equate to 11 gallon for $28.16\$28.16. Placing these calculated unit prices in ascending order provides the correct sequence.

Adım Adım Çözüm

1
Determine a common unit of measurement to compare all options.
The gallon is the most convenient common unit.
Converting all volumes to gallons allows for a direct dollar-to-dollar comparison of the unit prices.
2
Calculate the price per gallon for the 55-gallon drum.
$128.00÷5 gallons=$25.60\$128.00 \div 5 \text{ gallons} = \$25.60 per gallon.
Dividing the total cost by the total volume yields the unit price.
3
Calculate the price per gallon for the case of 11-quart bottles.
There are 44 quarts in a gallon, so four 11-quart bottles equal exactly 11 gallon. The price is $28.16\$28.16 per gallon.
Unit conversion is required before finding the price per gallon.
4
Calculate the price per gallon for the pack of 11-pint bottles.
There are 22 pints in a quart and 44 quarts in a gallon, so there are 88 pints in a gallon. Eight 11-pint bottles equal exactly 11 gallon. The price is $23.04\$23.04 per gallon.
Unit conversion is required to establish the total volume in gallons.
5
Calculate the price per gallon for the twin-pack of 11-gallon jugs.
$48.00÷2 gallons=$24.00\$48.00 \div 2 \text{ gallons} = \$24.00 per gallon.
Dividing the total cost by the total volume yields the unit price.
6
Compare the calculated prices per gallon and order them from lowest to highest.
$23.04<$24.00<$25.60<$28.16\$23.04 < \$24.00 < \$25.60 < \$28.16.
The question asks for the options to be arranged sequentially by increasing unit cost.

Anahtar Kavram

To compare the prices of items sold in different quantities and unit sizes, convert all volumes to a single common unit (such as gallons) and calculate the price per common unit for each option.
Soru 13Soru →

A maintenance supervisor is ordering floor sealant for a large building renovation. The sealant is available in two sizes: a 22-gallon jug priced at $18.00\$18.00, and a 11-quart bottle priced at $3.25\$3.25. If the renovation requires exactly 88 gallons of sealant, how much money is saved in total by purchasing the 22-gallon jugs instead of the 11-quart bottles?

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Cevap: $32.00\$32.00

Cevap

$32.00\$32.00
To find the total savings, calculate the total cost for each option. For the 22-gallon jugs, you need 44 jugs to reach 88 gallons (4×$18.00=$72.004 \times \$18.00 = \$72.00). For the 11-quart bottles, first convert 88 gallons to quarts (8×4=328 \times 4 = 32 quarts). You need 3232 bottles (32×$3.25=$104.0032 \times \$3.25 = \$104.00). The difference is $104.00−$72.00=$32.00\$104.00 - \$72.00 = \$32.00.

Adım Adım Çözüm

1
Calculate the total cost of purchasing 8 gallons using the 2-gallon jugs.
$72.00\$72.00
The project needs 8 gallons, which requires 4 jugs (8÷28 \div 2). At $18.00\$18.00 per jug, the cost is 4×$18.00=$72.004 \times \$18.00 = \$72.00.
2
Determine how many 1-quart bottles are needed to make 8 gallons.
32 bottles
There are 4 quarts in 1 gallon, so 8 gallons is equal to 32 quarts (8×48 \times 4).
3
Calculate the total cost of purchasing 32 quart bottles.
$104.00\$104.00
At $3.25\$3.25 per bottle, the cost is 32×$3.25=$104.0032 \times \$3.25 = \$104.00.
4
Calculate the total savings between the two options.
$32.00\$32.00
Subtract the lower bulk cost from the higher individual cost: $104.00−$72.00=$32.00\$104.00 - \$72.00 = \$32.00.

Anahtar Kavram

Unit Price Comparisons
Soru 14Soru →

A base landscaping crew needs to purchase concentrated herbicide. Vendor A sells a 55-gallon drum of the herbicide for $140.00\$140.00. Vendor B sells the same herbicide in 22-quart bottles for $15.00\$15.00 each. What is the difference in price per gallon, in dollars, between the two vendors?

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Cevap: 2

Cevap

The difference in price per gallon between the two vendors is 2 dollars.
By converting both options to a common unit price of dollars per gallon, we find Vendor A charges 28.00pergallonandVendorBcharges28.00 per gallon and Vendor B charges 30.00 per gallon. The difference between these unit prices is 30.00−30.00 - 28.00 = $2.00.

Adım Adım Çözüm

1
Calculate the price per gallon for Vendor A.
$140.00÷5 gallons=$28.00 per gallon\$140.00 \div 5 \text{ gallons} = \$28.00 \text{ per gallon}
To compare prices accurately, both must be expressed as a unit rate (price per gallon).
2
Convert the volume of Vendor B's bottles into gallons to find how many bottles equal one gallon.
Since there are 4 quarts4 \text{ quarts} in 1 gallon1 \text{ gallon}, a 22-quart bottle is 0.5 gallons0.5 \text{ gallons}. Therefore, it takes 22 bottles to make 1 gallon1 \text{ gallon}.
Unit prices must be in the same measurement (gallons) for a valid comparison.
3
Calculate the price per gallon for Vendor B.
$15.00×2 bottles=$30.00 per gallon\$15.00 \times 2 \text{ bottles} = \$30.00 \text{ per gallon}
This establishes the unit rate for Vendor B.
4
Find the difference between the two unit prices.
$30.00−$28.00=$2.00\$30.00 - \$28.00 = \$2.00
The question asks for the numeric difference in price per gallon.

Anahtar Kavram

Comparing unit prices by converting to a common unit of measure.
Soru 15Soru →

A motor pool sergeant is purchasing industrial degreaser for the vehicle maintenance bay. The facility requires exactly 88 gallons of degreaser. A supply catalog offers the degreaser in two sizes: a 11-gallon jug for $14.50\$14.50 and a 3232-ounce bottle for $4.00\$4.00. If the sergeant purchases the required amount using the most cost-effective option, how much money will be saved in total compared to buying the more expensive option?

Cevabı ve açıklamayı göster

Cevap: $12.00\$12.00

Cevap

$12.00\$12.00
The correct answer is found by first equalizing the volumes. There are 128 ounces in a gallon, so it takes four 32-ounce bottles to make a single gallon. Buying the degreaser in bottles costs 4 × 4.00=4.00 = 16.00 per gallon. The 1-gallon jug costs 14.50,meaningthejugsaves14.50, meaning the jug saves 1.50 per gallon compared to the bottles. Because the facility needs 8 gallons, the total savings is 8 × 1.50=1.50 = 12.00.

Adım Adım Çözüm

1
Determine the number of 32-ounce bottles needed to equal one gallon.
Since 11 gallon equals 128128 ounces, 128÷32=4128 \div 32 = 4 bottles per gallon.
To accurately compare prices, both options must be evaluated at the same unit of volume.
2
Calculate the price per gallon for the 32-ounce bottle option.
44 bottles ×$4.00=$16.00\times \$4.00 = \$16.00 per gallon.
This establishes a direct unit price comparison against the 1-gallon jug.
3
Determine which option is more cost-effective and calculate the savings per gallon.
The jug costs $14.50\$14.50 per gallon, which is $1.50\$1.50 cheaper than the $16.00\$16.00 per gallon cost of the bottles.
Finding the difference in unit price is necessary to calculate the total savings over the entire purchase.
4
Calculate the total savings for the required 8 gallons.
88 gallons ×$1.50=$12.00\times \$1.50 = \$12.00 total savings.
The facility requires 8 gallons, so the per-gallon savings must be multiplied by the total volume needed.

Anahtar Kavram

Comparing unit prices across different measurement units to find total purchase savings.
Unit Price Comparisons Alıştırma Soruları — Armed Services Vocational Aptitude Battery (ASVAB) | Examkin