# Math

Emily receives her paycheck. She spends 1/6 on food. She spends 3/5 of remaining amount on house payment. She spends 1/3 of what is left on her other bills. She spends 1/4 of the remaining money for entertainment. This activity leaves her with \$150. What was her original take home pay for the month?

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1. paycheck: x
food: 1/6 x, leaving 5/6 x
house: 3/5 of 5/6 x = 1/2 x, leaving 1/3 x
bills: 1/3 of 1/3 x = 1/9 x, leaving 2/9 x
entertainment: 1/4 * 2/9 x = 1/18 x, leaving 1/6 x

so, 150 = 1/6 x
x = 900

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