Chapter 6.7, Problem 37PPS

To determine

To find: Total number of boxes of each items received.

Answer to Problem 37PPS

Here, $\text{10}$ boxes of notebooks and $\text{6}$ boxes of mugs were received.

Explanation of Solution

Given:

Cost of one box of notebooks is $\$22$

Cost of one box of mugs is $\$40$

N spent t $\$460$

Calculation:

Let $u$ boxes of notebooks and $p$ boxes of mugs received.

As N counted total 16 boxes, thus, $u+p=16$ .

Cost of one box of notebooks is $\$22$ , cost of one box of mugs is $\$40$ and N spent $\$460$ , therefore this gives $22u+40p=460$ .

Thus the system of equation is

  $u+p=16$

  $22u+40p=460$

Solve the system of equations

  $\begin{array}{l}u+p=16\\ 22u+40p=460\\ \text{Multiply by 22 }\Rightarrow \text{ 22u + 22p = 352}\\ \Rightarrow \underset{\_}{\text{22u + 40p = 460}}\\ \text{subtract }\Rightarrow -\text{18p = }-\text{108}\\ \Rightarrow \text{ p = 6}\end{array}$

Put the value of $p$ in first equation

  $\begin{array}{l}\text{ u + 6 = 16}\\ \text{u = 16}-\text{6}\\ \text{u = 10 }\end{array}$

Hence $\text{10}$ boxes of notebooks and $\text{6}$ boxes of mugs were received.

Conclusion:

Therefore, $\text{10}$ boxes of notebooks and $\text{6}$ boxes of mugs were received.