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

Answer:

$4\ discs$

Step-by-step explanation:

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

Number of compact disc of $\ 7.50=y$

Total discs$=x+y$

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

$Cost\ of\ discs\ of\ \ 11.50=11.50\times number\ of\ discs=11.50\times x=11.50x\\\\Cost\ of\ discs\ of\ \ 7.50=7.50\times number\ of\ discs=7.50\times y=7.50y$

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

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

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

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