Chapter 2.4, Problem 16Q

a.

To determine

To write: and solve an inequality that represents number of weeks you need to save to purchase the bike.

Answer to Problem 16Q

  $x\ge 8$

Explanation of Solution

Let x denotes the number of weeks you need to save to purchase the bike.

It is given that you save $15 each week.

So, in x weeks you save $\$15x$ .

The minimum price of the bike is $120.

Now, to purchase the bike the amount saved must be at least equal to the minimum price.

Thus, the required inequality is:

  $\begin{array}{c}15x\ge 120\\ x\ge \frac{120}{15}\\ x\ge 8\end{array}$

Conclusion:

You need to save for at least 8 weeks.

b.

To determine

To write: and solve an inequality that represents number of weeks you need to save to purchase the bike.

Answer to Problem 16Q

  $x\ge \frac{11}{3}$

Explanation of Solution

Let x denotes the number of weeks you need to save to purchase the bike.

It is given that you save $15 each week.

So, in x weeks you save $\$15x$ .

Also, parents provided $65.

The minimum price of the bike is $120.

Now, to purchase the bike the sum of amount saved and the money provided by parents must be at least equal to the minimum price.

Thus, the required inequality is:

  $\begin{array}{c}65+15x\ge 120\\ 15x\ge 120-65\\ 15x\ge 55\\ x\ge \frac{11}{3}\end{array}$

Conclusion:

You need to save for at least $\frac{11}{3}$ weeks.