Question

3. Meghan earns money babysitting. She charges $5 an hour before

8 P.M. and $8 an hour after 8 P.M. She earned $26 for her last
babysitting job. Between what hours did Meghan babysit?

Answer 1

Let's call the number of hours before 8 P.M. that Meghan babysat "x", and the number of hours after 8 P.M. "y". We can set up two equations based on the information given:

5x + 8y = 26 (this is the total amount she earned)

x + y = total number of hours she babysat

We can solve for one of the variables in terms of the other and substitute it into the first equation:

y = total number of hours - x

5x + 8(total number of hours - x) = 26

5x + 8total number of hours - 8x = 26

3x = 26 - 8total number of hours

x = (26 - 8total number of hours)/3

Now we can try different values for the total number of hours she babysat to see if we get a whole number for x:

If she babysat for 1 hour, x = (26 - 8)/3 = 6, which is not a whole number.

If she babysat for 2 hours, x = (26 - 16)/3 = 3, which is a whole number.

If she babysat for 3 hours, x = (26 - 24)/3 = 0.67, which is not a whole number.

So we know she babysat for 2 hours before 8 P.M. and 1 hour after 8 P.M.:

5(2) + 8(1) = 18

2 + 1 = 3 total hours babysat

Therefore, Meghan babysat between 6 P.M. and 9 P.M.

Explanation: