Question

Mikasa earned money over the summer babysitting and dog walking. She was paid $15 an hour

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 brainly.com/question/24823220