Question

How do you solve this problem?

On black Friday 2017 Carmen paid $50 for 3 televisions and 5 radios.
Louis bought 5 TVs and 7 radios for $74. How much does each TV and radio cost?
(A) 7,5 (B) 5,7 (C) 8,6 (D)6,8

Answer 1

(B) 5,7

Explanation:

Suppose the cost of a TV is `$t`
and the cost of a radio is `$r`

We are told:
[1]`color(white)("XXX")3t+5r=50`
and
[2]`color(white)("XXX")5t+7r=74`

We can convert these equations so that the coefficient of `r` is identical
by multiplying everything in [1] by `7`
and multiplying everything in [2] by `5`

[3]`color(white)("XXX")21t+35r=350`
[4]`color(white)("XXX")25t+35r=370`

Subtracting [3] from [4] gives
[5]`color(white)("XXX")4t=20`

Then dividing [5] by `4`
[6]`color(white)("XXX")t=5`
A TV cost `$5`

Based on this we can substitute `5` for `t` in [1]
[7]`color(white)("XXX")3 * 5 +5r=50`

Simplifying:
[8]`color(white)("XXX")15+5r=50`

[9]`color(white)("XXX")5r=35`

[10]`color(white)("XXX")r=7`
A radio cost `$7`

In the sequence TV cost then radio cost
this corresponds to answer B