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.

Answer 1

Building and solving a system of equations, we find that:

a) The system is:

$b + w = 75$

$15b + 20w = 1350$

b) The solution is:

$b = 30, w = 45$

c) Replacing into the equations, we get:

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

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

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As stated in the problem:

• b is the number of hours babysitting.
• w is the number of hours walking dogs.

Item a:

Total of 75 hours, thus, the first equation of the system is:

$b + w = 75$

$15 for each hour babysitting, $20 for each hour walking the dog, and a total of $1350, thus:

$15b + 20w = 1350$

Then, the system of equations is:

$b + w = 75$

$15b + 20w = 1350$

Item b:

From the first equation, we write w as function of b, to find b in the second: $w = 75 - b$

Replacing in the second:

$15b + 20w = 1350$

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

$15b + 1500 - 20b = 1350$

$-5b = -150$

$5b = 150$

$b = \frac{150}{5}$

$b = 30$

Then, for w:

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

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

Item c:

To verify, we just replace the solutions into the two equations:

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

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

A similar problem is given at https://brainly.com/question/24823220