A specialized aerospace alloy is manufactured by combining titanium and aluminum in a rati… — Armed Services Vocational Aptitude Battery (ASVAB)

A specialized aerospace alloy is manufactured by combining titanium and aluminum in a ratio of $7:4$ by weight. If a batch of this alloy contains $140\text{ kilograms}$ of titanium, what is the total weight of the batch?

A
$80\text{ kg}$
$220\text{ kg}$ Answer
C
$245\text{ kg}$
D
$385\text{ kg}$

Answer

The total weight of the batch is

220\text{ kg}

The given ratio indicates the alloy consists of

7

parts titanium and

4

parts aluminum, making

11

parts in total. Because the

7

parts of titanium weigh

140\text{ kg}

, each single part weighs

20\text{ kg}

(

140 \div 7

). Multiplying the

11

total parts by

20\text{ kg}

per part results in a total weight of

220\text{ kg}

Step-by-Step Solution

Determine the weight of a single ratio part based on the known titanium content.

140\text{ kg} \div 7\text{ parts} = 20\text{ kg per part}

Since the ratio of titanium to aluminum is

7:4

, the

140\text{ kg}

corresponds exactly to the

7

parts of titanium.

Calculate the total number of parts in the alloy mixture.

7\text{ parts (titanium)} + 4\text{ parts (aluminum)} = 11\text{ total parts}

The total weight is composed of both the titanium and the aluminum parts combined.

Multiply the total number of parts by the weight of a single part.

11\text{ parts} \times 20\text{ kg per part} = 220\text{ kg}

This yields the combined weight of the entire batch.

Key Concept

Solving Part-to-Whole Ratio Problems

Estimated Time:1m 0s

Question

Answer

Step-by-Step Solution

Key Concept

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