Manny works 40 hours per week. He must work for his parents where he earns $8 per hour. He also works for a computer company where he earns 20$ per hour. How many hours can Manny work for the computer company to earn a total of $464 per week from both jobs?

x - number of working hours for parents

y - number of working hours for a computer company

{x + y = 40

{8x + 20y = 464

{x = 40 - y

{8 (40 - y) + 20y = 464 || : 4

{x = 40 - y

{2 (40 - y) + 5y = 116

{x = 40 - y

{80 - 2y + 5y = 116

{x = 40 - y

{80 + 3y = 116 || - 80

{x = 40 - y

{3y = 36 || : 3

{x = 40 - y

{y = 12

{x = 40 - 12

{y = 12

{x = 28

{y = 12

12 Hours

Step-by-step explanation:

Set up a system of equations

20x + 8y = 464

x + y = 40

Solve with substitution

1. Solve x + y = 40 for x:

x + y = 40

x + y + - y = 40 + - y (Add - y to both sides)

x = - y + 40

2. Substitute - y + 40 for x in 20x + 8y = 464:

20x + 8y = 464

20 (-y + 40) + 8y = 464

-12y + 800 = 464 (Simplify both sides of the equation)

-12y + 800 + - 800 = 464 + - 800 (Add - 800 to both sides)

-12y = - 336

-12y : - 12 = - 336 : - 12 (Divide both sides by - 12)

y = 28

3. Substitute 28 for y in x = - y + 40:

x = - y + 40

x = - 28 + 40

x = 12 (Simplify both sides of the equation)

Answer:

x = 12 and y = 28