# Jacques can buy six CDs and three video cassettes for $163.7 or he can buy nine CDs and two video cassettes for$200.53. How do you find the price of one video cassette?

Nov 29, 2016

I got: $18.01 for the VHS and $18.28 for the CDs.

#### Explanation:

Let us call the price of CDs $c$ and of the Videos $v$; we can write:
$6 c + 3 v = 163.7$
$9 c + 2 v = 200.53$

we can isolate $c$ from the first and substitute into the second:
$c = \frac{163.7 - 3 v}{6}$
and:
$9 \frac{163.7 - 3 v}{6} + 2 v = 200.53$
$1473.3 - 27 v + 12 v = 1203.18$

$v = 18.01$

and so:

$c = \frac{163.7 - 3 \cdot 18.01}{6} = 18.28$

Considering that nowadays it is almost impossible to find video cassettes and even CDs are difficult to come by....I suspect the exercise is quite old!