Hard ACT Question

Algebra Level 1

For all real numbers b b and c c such that the product of 3 and c c is b b , which of the following expressions represents the sum of c c and 3 in terms of b b ?

b + 3 b+3 b + 3 3 \frac{b+3}3 3 b + 9 3b+9 b 3 + 3 \frac b3 + 3 3 b + 3 3b+3

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Finn C by Finn C , 18, USA

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2 solutions

Hung Woei Neoh
Jun 2, 2016

Relevant wiki: Setting Up Equations

3 c = b c = b 3 3c = b\\ c=\dfrac{b}{3}

Therefore,

c + 3 = b 3 + 3 c+3 = \dfrac{b}{3} + 3

The answer is E \boxed{\text{E}}

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My solution is look above ^.... :D

Finn C - 5 years ago

The first equation is b = 3 c b=3c . Solving for c c in terms of b b (divide both sides by 3), we get c = b 3 c=\dfrac{b}{3} .

The expression desired is

c + 3 = b 3 + 3 c+3= \dfrac{b}{3} + 3 (just substitute)

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