A tailor is combining two pieces of fabric to make a continuous banner. One piece is 3 \fr… — Armed Services Vocational Aptitude Battery (ASVAB)

A tailor is combining two pieces of fabric to make a continuous banner. One piece is $3 \frac{1}{2}$ yards long, and the second piece is $1 \frac{1}{4}$ yards long. After joining them together end-to-end, the tailor needs to cut the combined fabric into smaller segments that are each $15$ inches long. How many complete segments can the tailor cut from the combined fabric?

11Answer
B
10
C
9
D
3

Answer

The total length of the fabric is found by adding

3 \frac{1}{2}

yards and

1 \frac{1}{4}

yards, which equals

4 \frac{3}{4}

yards. Because there are

36

inches in one yard, this is equivalent to

4.75 \times 36 = 171

inches. Dividing the total

171

inches by the required segment length of

15

inches gives

11.4

. Therefore,

11

complete segments can be cut.

Step-by-Step Solution

Calculate the total length of the fabric in yards.

3 \frac{1}{2} + 1 \frac{1}{4} = 3 \frac{2}{4} + 1 \frac{1}{4} = 4 \frac{3}{4} \text{ yards}

The two pieces are joined end-to-end, requiring addition with a common denominator.

Convert the total length from yards to inches.

4 \frac{3}{4} \text{ yards} \times 36 \text{ inches/yard} = 171 \text{ inches}

The target segment length is in inches, so the total fabric length must share the same unit before dividing.

Divide the total inches by the length of one segment.

171 \div 15 = 11.4

Division determines how many

15

-inch segments fit into the

171

-inch length.

Identify the number of complete segments.

11

The tailor can only use whole, complete segments, so the decimal remainder is dropped.

Key Concept

Multi-step conversion of US customary linear units involving mixed fractions.

Estimated Time:1m 15s

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