Question

You are working two part-time jobs. Working at the local library pays $15 per hour and working as a

personal trainer pays $20 per hour. Last week you made $800 and worked 45 total hours.
1. Find out how many hours you worked at each job.

Answer 1

20 hours worked at the local library.

25 hours worked as a personal trainer.

Explanation:

Definition of the variables:

• Let x = number of hours worked at the local library.
• Let y = number of hours worked as a personal trainer.

Given information:

• Working at the local library pays $15 per hour.
• Working as a personal trainer pays $20 per hour.
• Last week you made $800 and worked 45 total hours.

Create a system of equations using the defined variables and the given information:

`\begin{cases}15x+20y=800\\x+y=45\end{cases}`

Rearrange the second equation to make y the subject:

`\implies y=45-x`

Substitute this into the first equation and solve for x:

`\implies 15x+20(45-x)=800`

`\implies 15x+900-20x=800`

`\implies -5x+900=800`

`\implies -5x+900-900=800-900`

`\implies -5x=-100`

`\implies 5x=100`

`\implies 5x / 5=100/ 5`

`\implies x=20`

Substitute the found value of x into the second equation and solve for y:

`\implies 20+y=45`

`\implies 20+y-20=45-20`

`\implies y=25`

Therefore:

• 20 hours worked at the local library.
• 25 hours worked as a personal trainer.

Answer 2

• 20 hours at library and 25 hours as a trainer

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Let the hours at library be l and hours as trainer be t.

Set equations

Total hours

• l + t = 45 ⇒ l = 45 - t

Total payment

• 15l + 20t = 800 ⇒ 3l + 4t = 160

Solve by substitution

• 3(45 - t) + 4t = 160
• 135 - 3t + 4t = 160
• t = 160 - 135
• t = 25

Find l

• l = 45 - 25
• l = 20