Question

Mika’s gym allows her to bring 3 guests for free. After the first three, she must pay $7 per guest. How many guests, g, can she bring to the gym if she pays $42?

Three of these equations give the correct value of g. Which equation does NOT?

A 7g = 63
B 7(g – 3) = 42
C 7g – 3 = 42
D g = 9
all help is appreciated

Answer 1

well the brute-force-y method would be to just solve each equation for g and see which one gives you the different solution. but that's missing the point of what the question is trying to teach.

she gets three free guests. so let's say she wants to bring 4 guests, she only has to pay for 4 - 3 = 1 guest. same logic for 5 guests, she only has to pay for 5 - 3 = 2 guests.

so from this pattern, we can deduce that she has to pay for g - 3 guests. now, each of those g - 3 guests costs 7 dollars, right? so based on that, what would be the expression that represents the cost of those guests?