Chapter 6, Problem 9PT

To determine

To find: The number of pairs of jeans and sweaters the person S bought.

Answer to Problem 9PT

The person S bought 2 pairs of jeans and 5 sweaters.

Explanation of Solution

Given information:

The person S has $ 300 to buy jeans and sweaters. A jeans costs $65 and sweaters costs $34. She buys 7 items.

Method used:

According to given conditions a system of equations is obtained and then solved.

Calculations:

Let x and y be the number of pairs of jeans and sweaters, shell bought.

Since, total $300 amount of money is spent, therefore,

  $65x+34y=300$  ...... (1)

The total 7 items are purchased, therefore,

  $x+y=7$  ...... (2)

Now, multiplying equation (2) by 65 and subtracting from equation (1)

  $\left(65x+34y\right)-65\left(x+y\right)=300-\left(65\times 7\right)$

  $\Rightarrow 65x+34y-65x-65y=300-455$

  $\Rightarrow \cancel{65x}+34y-\cancel{65x}-65y=-155$

  $\Rightarrow -31y=-155$

  $\Rightarrow y=\frac{-155}{-31}=5$

Thus, a sweaters costs $5.

Now, substituting $y=5$ in equation (2)

  $x+y=7$

  $\Rightarrow x+5=7$

  $\Rightarrow x=7-5=2$

Thus, a pairs of jeans costs $2.

Conclusion:

The person S bought 2 pairs of jeans and 5 sweaters.