Basic Ratios

22 questions

All types22 Multiple choice11 Numeric5 Matching6

A defense contractor manufactures three types of vehicle armor panels: Type A, Type B, and Type C. The ratio of Type A panels to Type B panels produced is $2:3$ . The ratio of Type B panels to Type C panels produced is $4:5$ . If the contractor produces a total of $1,400$ panels across all three types, how many Type C panels are produced?

320

500

600

1,000

Show answer & explanation

Answer: 600

Answer

600

To find the number of Type C panels, the two separate ratios must first be combined into one continuous ratio. Since Type B is in both ratios (

3

parts in the first,

4

parts in the second), we find a common multiple, which is

12

. Scaling the ratios gives Type A : Type B =

8:12

and Type B : Type C =

12:15

. Combined, the ratio is

8:12:15

. Adding these gives

35

total parts. Dividing the

1,400

total panels by

35

reveals each part equals

40

panels. Because Type C represents

15

of those parts, we multiply

15

40

to get

600

Type C panels.

Step-by-Step Solution

Identify the overlapping category (Type B) in both given ratios and find the least common multiple for its values (

3

and

4

The least common multiple of

3

and

4

12

To compare all three panel types simultaneously, they must be expressed within a single, unified ratio sequence.

Scale both original ratios so that Type B is represented by

12

in both.

Multiply the first ratio (

2:3

) by

4

to get

8:12

. Multiply the second ratio (

4:5

) by

3

to get

12:15

Multiplying both sides of a ratio by the same number keeps the proportions mathematically equivalent.

Combine the scaled ratios into a single three-part ratio and calculate the total number of parts.

The unified ratio of Type A to Type B to Type C is

8:12:15

. The total number of parts is

8 + 12 + 15 = 35

The total number of parts represents the entire production batch in ratio units.

Divide the total actual number of panels by the total ratio parts to find the value of one part, then calculate the total for Type C.

1,400 \div 35 = 40

panels per part. Type C has

15

parts, so

15 \times 40 = 600

Type C panels.

This scales the ratio back up to the real-world quantities provided in the problem stem.

Key Concept

Combining Overlapping Ratios

Estimated Time:1m 30s

Question 22Question →

Match each military personnel or equipment scenario to its correctly simplified part-to-part ratio.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The correct matches simplify each starting ratio by finding the greatest common divisor for both terms in the specified order.

Each scenario describes a straightforward part-to-part relationship. By arranging the quantities in the requested order and dividing both numbers by their greatest common divisor, we arrive at the simplest equivalent ratio for each match.

Step-by-Step Solution

Identify the initial quantities in the specific order requested by each scenario.

20:5 for trucks to command vehicles; 6:18 for medics to infantry; 10:15 for water to food; 12:8 for officers to enlisted.

Establishing the correct order is strictly required to prevent inverted ratios.

Determine the greatest common divisor (GCD) for each pair of numbers.

The GCD for 20 and 5 is 5. The GCD for 6 and 18 is 6. The GCD for 10 and 15 is 5. The GCD for 12 and 8 is 4.

Dividing by the GCD reduces the ratio to its lowest, simplest form.

Divide both terms of each raw ratio by their respective GCD.

20:5 becomes 4:1. 6:18 becomes 1:3. 10:15 becomes 2:3. 12:8 becomes 3:2.

This calculation yields the final simplified part-to-part ratio for each scenario, which directly pairs with the right-hand items.

Key Concept

Simplifying part-to-part ratios

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Basic Ratios

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes