Question

Maddy and her cousin work during the summer for a landscaping company. Maddy’s cousin has been working for the company longer, so her pay is 30% more than Maddy’s. Last week, Maddy’s cousin worked 27 hours, and Maddy worked 23 hours. Together, they earned $493.85. What is Maddy’s hourly pay?

Answer 1

Maddy's hourly pay is $8.50

Explanation:

First, we need to use the information given to us to form a system of equations to determine either Maddy's pay, or her cousin's pay. In this case, we are interested in Maddy's pay.

We know her cousin makes 30% more than Maddy, which means she makes 100% of what Maddy makes, and an additional 30%. So we have our first equation:

C = M + .3M = 1.3M, where C is the amount the cousin makes and M is Maddy's pay.

The second piece of information is that in one week, Maddy worked 23 hours, and her cousin worked 27, and together they made $493.85. So now we have our second equation:

27C + 23M = 493.85, where C is the amount the cousin makes and M is the amount Maddy makes.

Now we simply substitute are value of C from the first equation into the second equation like such:

27(1.3M) + 23M = 493.85

And now we solve for M to find Maddy's pay.

27(1.3M) + 23M = 493.85

35.1M + 23M = 493.85

58.1M = 493.85

M = 8.5

To verify our answer is correct, let's find the value of money earned per hour by the cousin using the first equation:

C = 1.3(8.5) = 11.05

Now let's see if the number of hours worked by each and their pay adds up to the 493.85 from the previous week:

27(11.05) + 23(8.5) =? 493.85

298.35 + 195.5 =? 493.85

493.85 == 493.85

So, now we have confirmed that Maddy makes $8.50 per hour, and her cousin makes $11.05 per hour.

Cheers.