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.
Please help!!!

Answer 1

Using a system of equations, it is found that:

a)

$b + w = 75$

$15b + 20w = 1350$

b)

The solution is $b = 30, w = 45$

c)

$b + w = 75 \rightarrow 30 + 45 = 75 \rightarrow 75 = 75$

$15b + 20w = 1350 \rightarrow 15(30) + 20(45) = 1350 \rightarrow 1350 = 1350$

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Item a:

Total of 75 hours, thus:

$b + w = 75$

She was paid $15 an hour babysitting and $20 an hour dog walking. Earned a total of $1350, thus:

$15b + 20w = 1350$

-------------------------------------

Item b:

To solve for w, from the first equation:

$b = 75 - w$

Replacing into the second:

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

$1125 - 15w + 20w = 1350$

$5w = 225$

$w = \frac{225}{5}$

$w = 45$

Then, for b:

$b = 75 - w = 75 - 45 = 30$

-------------------------------------

Item c:

Replacing b and w into the equations:

$b + w = 75 \rightarrow 30 + 45 = 75 \rightarrow 75 = 75$

$15b + 20w = 1350 \rightarrow 15(30) + 20(45) = 1350 \rightarrow 1350 = 1350$

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