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

1 Answer
Dec 8, 2017

(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