Chapter 1.4, Problem 48E

a.

To determine

To write: and solve an absolute value equation to find the maximum and minimum acceptable soccer ball weights.

Answer to Problem 48E

  $\left|x-430\right|=20$

  $410\text{ gm, 450 gm}$

Explanation of Solution

Let x denotes the percent soccer ball weight.

Now, it is given that the recommended weight is 430 gm but it can vary up to 20 gm.

Thus, the absolute value equation representing the given solution is:

  $\left|x-430\right|=20$

It is equivalent to:

  $x-430=\pm 20$

Now,

  $\begin{array}{c}x-430=20\\ x=20+430\\ x=450\end{array}$

Or

  $\begin{array}{c}x-430=-20\\ x=-20+430\\ x=410\end{array}$

Check:

  $\begin{array}{c}\left|450-430\right|=20\\ \left|20\right|=20\\ 20=20\end{array}$

And

  $\begin{array}{c}\left|410-430\right|=20\\ \left|-20\right|=20\\ 20=20\end{array}$

Both the statements are true.

Conclusion:

Thus, the maximum and minimum acceptable soccer ball weights are 450 gm and 410 gm respectively.

b.

To determine

if a soccer ball which initially weigh 423 gm and after wear and tear whose weight is reduced by 16 gm is still acceptable or not.

Answer to Problem 48E

No, that ball is not acceptable

Explanation of Solution

The actual weight of the ball = 423 gm

The current weight of the ball $=423-16=407gm$

But from part (a), the acceptable range of weight is 410 gm to 450 gm.

Clearly, 407 gm doesn’t lie in this range.

Thus, the ball is not acceptable.