Chapter 1.1, Problem 74SPR

To determine

To calculate the price of shirt and slacks

Answer to Problem 74SPR

The solution is $x=12$ and $y=18$

Explanation of Solution

Given information:

Day 1, 3 shirts and 2 pairs of slacks are bought for $72.

Day 2, 2 shirts and 4 pair of slacks are bought for $96.

The system of equation for day 1 and day 2 are,

  $\begin{array}{l}3x+2y=72,\\ 2x+4y=96\end{array}$

Calculation:

In first equation, writing x in terms of y.

Shifting the terms,

  $3x=72-2y$

Cross-multiplying,

  $x=\frac{72}{3}-\frac{2y}{3}$

On solving,

  $x=24-\frac{2y}{3}$ ____________(1)

Substituting the value in equation 2,

  $2(24-\frac{2y}{3})+4y=96$

On solving,

  $48-\frac{4y}{3}+4y=96$

Shifting the terms,

  $\frac{8y}{3}=96-48$

On solving,

  $\frac{8y}{3}=48$

Cross- multiplying,

  $y=\frac{48\times 3}{8}$

On solving,

  $y=18$

Substituting the values in (1),

  $x=24-\frac{2(18)}{3}$

On solving,

  $x=12$

Hence, the solution is

  $x=12$ and $y=18$