Chapter 6, Problem 9PT

To determine

the number of pairs of jeans and sweaters bought.

Answer to Problem 9PT

The cost of one jean is: $\$3$ and the cost of one sweater is: $\$5$

Explanation of Solution

Given:

S has $175

Cost of jean $25,

Cost of sweater $20,

S buys 8 items

Calculation:

Assume the cost for one jean is $x$ and the cost for one sweater is $y$ respectively.

Here the equations are:

  $x+y=8$

  $x=8-y\dots \dots (1)$

And,

  $25x+20y=175\dots \dots (2)$

The strategy is to find the cost of each items.

Substitute the value of $x$ in equation (2) to get

  $25(8-y)+20y=175$

  $200-25y+20y=175$

  $200-5y-200=175-200$

  $-5y=-25$

  $\frac{5y}{5}=\frac{25}{5}[$ Divide both sides by 5]

  $y=5$

Again, from equation ( 1 ),

  $x=8-5$

  $x=3$

Hence, the cost of one jeans is: $\$3$ and the cost of one sweater is: $\$5$

Conclusion:

Hence, the cost of one jeans is: $\$3$ and the cost of one sweater is: $\$5$