GMAT Word Problems Explained — Beth, Naomi, and Juan raised a total of 55USD for charity. Naomi

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?

word problemslinear equationstranslations

Explanation	Calculations	Help
$We name B as the amount Beth raised, J as the amount Juan raised, and N as the amount Naomi raised.$	$B = amount Beth raised, J = amount Juan raised, N = amount Naomi raised$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate "Juan raised twice as much as Beth" into an equation.$	$J = 2 B$	Theory & Tactics Method Card TRANS1-E Click to view full details
$We translate "Naomi raised 5USD less than Juan" into an equation.$	$N = J - 5$	Theory & Tactics Method Card TRANS1-D Click to view full details
$We translate "raised a total of 55USD for charity" into an equation.$	$B + J + N = 55$	Theory & Tactics Method Card TRANS1-C Click to view full details Theory & Tactics Method Card TRANS1-B Click to view full details
$We substitute the expressions for J and N into the total equation.$	$B + 2 B + (2 B - 5) = 55$	Theory & Tactics Method Card EQUA3-A Click to view full details
$We simplify and solve the resulting equation to find B .$	$5 B - 5 = 55 5 B = 60 B = 12$	Theory & Tactics Method Card EQUA1-A Click to view full details

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Beth raised 12USD.