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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 $$ t$ $$t$
and the cost of a radio is $$ r$ $$r$

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

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

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

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

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

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

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

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

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

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

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