Beth, Naomi, and Juan raised a total of 55USD for charity. Naomi raised 5USD less than Juan, and...

Question

Beth, Naomi, and Juan raised a total of 55USD for charity. Naomi raised 5USD less than Juan, and Juan raised twice as much as Beth. How much did Beth raise?

GMAT Panda · Accepted Answer

Beth raised 12USD. We name B as the amount Beth raised, J as the amount Juan raised, and N as the amount Naomi raised. B = amount Beth raised, J = amount Juan raised, N = amount Naomi raised We translate "Juan raised twice as much as Beth" into an equation. J = 2B We translate "Naomi raised 5USD less than Juan" into an equation. N = J - 5 We translate "raised a total of 55USD for charity" into an equation. B + J + N = 55 We substitute the expressions for J and N into the total equation. B + 2B + (2B - 5) = 55 We simplify and solve the resulting equation to find B. 5B - 5 = 55 5B = 60 B = 12

Explanation	Calculations	Help
$We name B as the amount Beth raised, J as the amount Juan raised, and N as the amount Naomi raised.$	$B = amount Beth raised, J = amount Juan raised, N = amount Naomi raised$
$We translate "Juan raised twice as much as Beth" into an equation.$	$J = 2 B$
$We translate "Naomi raised 5USD less than Juan" into an equation.$	$N = J - 5$
$We translate "raised a total of 55USD for charity" into an equation.$	$B + J + N = 55$
$We substitute the expressions for J and N into the total equation.$	$B + 2 B + (2 B - 5) = 55$
$We simplify and solve the resulting equation to find B .$	$5 B - 5 = 55 5 B = 60 B = 12$

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