A DJ found a music store that had a great collection of used CD's. he purshased 38 CD's for a total of $235. The purchase included CD's priced at either $5.00 or $8.00. How many CD's in each price category did the DJ buy?

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- Mar 5th 2006, 08:15 AM #1

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- Mar 5th 2006, 08:54 AM #2Originally Posted by
**wild_flowr69**

$\displaystyle 5x+8y=235$.

Additionally, we know that 38 CDs were bought, so:

$\displaystyle x+y=38$.

Two equations, two unknowns, so you can solve for x and y.

-Dan

- Mar 5th 2006, 09:53 AM #3

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Let me continue from topsquark's solution:

The equations

$\displaystyle \left\{\begin{array}{cc}5x+8y&=235\\x+y&=38\end{ar ray}\right$

In the second equation solve for $\displaystyle y$:

$\displaystyle y=38-x$

Substitute that into the first:

$\displaystyle 5x+8(38-x)=235$

Now solve it,

$\displaystyle 5x+304-8x=235$

Thus,

$\displaystyle -3x=-69$

Thus,

$\displaystyle x=23$

Thus,

$\displaystyle y=15$