Question

Mikasa earned money over the summer babysitting and dog walking. She was paid $15 an hour babysitting and $20 an hour dog walking. If she worked a total of 75 hours over the summer and earned a total of $1350, how many hours did she work at each job?
a. (2 pts) Set up the system of equations for this scenario. Let “b” represent hours babysitting and “w” represent hours walking dogs.
b. (2 pts) Solve the system of equations. Show how you got your solution.
c. (2 pts) Show your solution works in both the original equations.

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Answer 1

The two equation are $b+w=75$ and $15b+20w=1350$.

She worked $30$ hours as babysitting and $45$ hours dog walking.

And, the solution works in both the equations.

A) Let “$b$” represent hours babysitting and “$w$” represent hours walking dogs.

She worked a total of $75$ hours. So, $b+w=75...(i)$

She was paid $$15$ an hour babysitting and $$20$ an hour dog walking and earned a total of $$1350$,

$15b+20w=1350...(ii)$

B)

$b+w=75...(i)$

$b=75-w$

Put this value in $(ii)$

$15(75-w)+20w=1350$

$1125-15w+20w=1350$

$5w=1350-1125$

$5w=225$

$w=45$

Put this value in $(i)$

$b+45=75$

$b=75-45$

$b=30$

So, she worked $30$ hours as babysitting and $45$ hours dog walking.

C)

Substituting the values in $(i)$,

$b+w=75$

$30+45=75$

$75=75$, which is true

Substituting the values in $(ii),$

$15b+20w=1350$

$15\times 30+20\times 45=1350$

$450+900=1350$

$1350=1350$, which is true

So, the solution works in both the equations.

Learn more about linear equations in two variables here:

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