Question

Challenge The plastic tips on the ends of a shoelace are called aglets. Suppose a sneaker factory produces p pairs of shoes each hour and is in operation for h hours each day. Write a variable expression for the number of single aglets the factory uses each day. Evaluate the expression when $p=200\text{and}h=20$. Explain what your answer means.

Short answer

The variable expression for number of single aglets the factory uses each day is $4·p·h$.

The number of single aglets the factory uses each day when $p=200\text{and}h=24$ is obtained as:

$4·200·24=19200$

Step-by-step solution

Step-1 – Apply the concept of Variable

In any expression or equation, the variable is an unknown quantity. It may be any alphabet or any special symbol.

Step-2 – Given

Aglet is the plastic tips which is attached on the ends of a shoelace.

Number of pairs of shoes produces each hour is $p$.

Number of hours of operation, the factory operates each day is $h$.

Step-3 – Explanation

In one shoe, number of aglet use is 2.

Number of aglets use in one pair of shoes is $2·2=4$.

Total number of pairs of shoes produce in one day is $p·h$.

Hence, the variable expression for number of single aglets the factory uses each day is obtained as:

$4·p·h$

Now, if $p=200\text{and}h=24$, then the number of single aglets the factory uses each day is obtained as:

$4·200·24=19200$

Hence, the variable expression for number of single aglets the factory uses is the product of number of aglet used in one show, number of pair of shoe produce in one hour and total number of hours the factory operates.