Question

A construction worker is building a wall. The wall is 17.5 yds long. He needs to place a stud every 15 inches. The first stud has already been placed at one end of the wall. How many additional studs are needed, if the last stud will be placed at the other end of the wall? First fill in the blanks on the left side using the ratios shown. Then write your answer.

Answer 1

The correct answers are:

Box-1: $\frac{3\thinspace ft}{1\thinspace yd}$

Box-2: $\frac{12\thinspace \thinspace in}{1\thinspace ft}$

Box-3: $\frac{1\thinspace stud}{15\thinspace in}$

Box-4: 42 studs

Explanation:

Given:

Wall is 17.5 yds long.

In 1 yard, there are 3 feet.

Therefore,

$\frac{17.5\thinspace yd}{1} * \frac{3\thinspace ft}{1\thinspace yd}$

In Box-1, you should put $\frac{3\thinspace ft}{1\thinspace yd}$.

In 1 foot, there are 12 inches.

Therefore,

$\frac{17.5\thinspace yd}{1} * \frac{3\thinspace ft}{1\thinspace yd}*\frac{12\thinspace in}{1\thinspace ft}$

In Box-2, you should put $\frac{12\thinspace \thinspace in}{1\thinspace ft}$.

He needs to place 1 stud every 15 inches.

Therefore,

$\frac{17.5\thinspace yd}{1} * \frac{3\thinspace ft}{1\thinspace yd}*\frac{12\thinspace in}{1\thinspace ft}*\frac{1\thinspace stud}{15\thinspace in}$

In Box-3, you should put $\frac{1\thinspace stud}{15\thinspace in}$.

Now multiple all the numbers, you will get the number of studs.

$\frac{17.5\thinspace yd}{1} * \frac{3\thinspace ft}{1\thinspace yd}*\frac{12\thinspace in}{1\thinspace ft}*\frac{1\thinspace stud}{15\thinspace in} = 42\thinspace studs$

In Box-4, write 42 studs.

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