Answer:
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
