Question

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?

Answer 1

Answer:

• $ 900

Explanation:

Translate every word sentence into an algebraic operation or expression to find and solve an equation:

1) Name the variable:

• Let x be Emily's original take-home pay: x

2) She spends 1/6 of it on food means:

• spending: 1/6 of x = (1/6)x = x/6

• remaining: x - x/6 = (6x - x) / 6 = 5x/6

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

• spending: 3/5 of 5x/6 = (3/5) . (5x/6) = 3x/6 = x/2

• remaining: 5x/6 - x/2 = (5x - 3x)/6 = 2x/6 = x/3

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

• spending: 1/3 of x/3 = (1/3) . (x/3) = x/9

• remaining: x/3 - x/9 = (3x - x)/9 = 2x/9

5) Finally, she spends 1/4 of the remaining money for entertainment:

• spending: 1/4 of 2x/9 = (1/4) . (2x/9) = 2x/36 = x/18

• remaining: 2x/9 - x/18= (4x - x)/18 = 3x/18 = x/6

6) This activity leaves her with $150:

• x/6 = 150

Solve for x:

• Multiply both sides by 6: x = 900.

Answer: Her original take - home pay was $ 900