Emily receives her paycheck for the month. she spends 1/6 of it on food. she then spends
3/5 of what remains on her house payment. she spends 1/3 of what is then left for her
other bills. finally, she spends 1/4 of the remaining money for entertainment. this
activity leaves her with $150, that she puts into savings. what was her original take-
home pay?

The amount of the Emily's paycheck for the month was $900

She spend on her house payment $450

Step-by-step explanation:

Let

x > amount of the Emily's paycheck for the month

we know that

1) She spends 1/6 of it on food

She spend (1/6)x on food

The remaining money is [x-(1/6)x]=(5/6)x

2) She then spends  3/5 of what remains on her house payment.

She spend on her house payment (3/5)[(5/6)x]=(1/2)x

The remaining money is (1-3/5)[(5/6)x]=2/5[(5/6)x]=(1/3)x

3) She spends 1/3 of what is then left for her  other bills

She spends in other bills (1/3)[(1/3)x]=(1/9)x

The remaining money is (1-1/3)[(1/3)x]=(2/3)[(1/3)x]=(2/9)x

4) She spends 1/4 of the remaining money for entertainment

She spends for entertainment (1/4)[(2/9)x]=(2/36)x

The remaining money is (1-1/4)[(2/9)x]=(3/4)[(2/9)x]=(1/6)x

we know that

(1/6)x=150

Solve for x

x=150*6=$900

therefore

The amount of the Emily's paycheck for the month was $900

She spend on her house payment (1/2)x

(1/2)x=(1/2)900=$450