Question

A music store is selling compact disc for $11.50 and $7.50. You buy 12 discs and you spend a total of $106. How many compact discs that cost $11.50 did you buy?

Answer 1

`4\ discs`

Explanation:

Let number of compact disc of
`\$11.50=x`

Number of compact disc of
`\$ 7.50=y`

Total discs
`=x+y`

`x+y=12\ \ \ ..............(1)`

`Cost\ of\ discs\ of\ \$11.50=11.50* number\ of\ discs=11.50* x=11.50x\\\\Cost\ of\ discs\ of\ \$7.50=7.50* number\ of\ discs=7.50* y=7.50y`

`Total\ cost=11.50x+7.50y\\\\11.50x+7.50y=106\ \ ............(2)`

`Solve\ x+y=12\\\\11.50x+7.50y=106`

`Equation(2)-7.50* Equation(1)\\\\11.50x-7.50x+7.50y-7.50y=106-7.50* 12\\\\4x=106-90\\\\4x=16\\\\x=4`

Number of compact discs having cost
`\$11.50=4`