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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.

Respuesta :

mhanifa

Answer:

  • 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
semsee45

Answer:

20 hours worked at the local library.

25 hours worked as a personal trainer.

Step-by-step 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:

[tex]\begin{cases}15x+20y=800\\x+y=45\end{cases}[/tex]

Rearrange the second equation to make y the subject:

[tex]\implies y=45-x[/tex]

Substitute this into the first equation and solve for x:

[tex]\implies 15x+20(45-x)=800[/tex]

[tex]\implies 15x+900-20x=800[/tex]

[tex]\implies -5x+900=800[/tex]

[tex]\implies -5x+900-900=800-900[/tex]

[tex]\implies -5x=-100[/tex]

[tex]\implies 5x=100[/tex]

[tex]\implies 5x \div 5=100\div 5[/tex]

[tex]\implies x=20[/tex]

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

[tex]\implies 20+y=45[/tex]

[tex]\implies 20+y-20=45-20[/tex]

[tex]\implies y=25[/tex]

Therefore:

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

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