Question

Alexander is working two summer jobs, making $10 per hour washing cars and $8 per hour landscaping. Last week Alexander worked twice as many hours washing cars as he worked landscaping and earned a total of $84. Write a system of equations that could be used to determine the number of hours Alexander worked washing cars last week and the number of hours he worked landscaping last week. Define the variables that you use to write the system.

Answer 1

Let C= the number of hours spent washing cars

Let L= the number of hours spent landscaping

The system of equations is

{10C+8L=84

{C=2L

Alexander spent 3 hours landscaping and 6 hours washing cars

Explanation:

Let variable C= the number of hours spent washing cars, and let L=the number of hours spent landscaping.

Since Alexander makes $10 per hour washing cars, the expression will be 10C. For landscaping, the expression is 8L.

The total money he makes is 84, so the equation will be 10C+8L=84

C=2L is the equation of time spent working on cars vs landscaping.

The system of equations is

{10C+8L=84

{C=2L

We can solve by substitution, substitute 2L in for C in the first equation.

10(2L)+8L=84

Now simplify and solve

20L+8L=84

28L=84

L=3

Put 3 in for L

C=2(3)

C=6

Alexander spent 3 hours landscaping and 6 hours washing cars

Answer 2

Let
`\sf \boxed{\; x \;}` = Number of hours Alexander worked washing cars

Let
`\sf \boxed{\; y \;}` = Number of hours Alexander worked landscaping

System of equations:

`\sf \begin{cases} x = 2y \\ 10x + 8y = 84 \end{cases}`

Explanation:

Let x be the number of hours Alexander worked washing cars and y be the number of hours he worked landscaping.

Given that Alexander worked twice as many hours washing cars as landscaping, the first equation is:

`\sf x = 2y`

The second equation represents the total earnings, which is the sum of the earnings from washing cars and landscaping, and it is equal to $84:

`\sf 10x + 8y = 84`

So, the system of equations is:

`\sf \begin{cases} x = 2y \\ 10x + 8y = 84 \end{cases}`

These equations describe the relationship between the number of hours Alexander worked washing cars ( x ) and landscaping ( y ), taking into account both the hourly rates and the total earnings.