Question

Desmond wants to pay Andrea $5 more an hour than he pays Max. Desmond has a budget of $250. He has decided Andrea will work 10 hours and Max will work 15 hours. Create a system of equations that will help Desmond determine Andrea's hourly rate, a, and Max's hourly rate, m.

Answer 1

a-5=m

10a+15m = $250

Andreas hourly rate is $13 while that of Max is $8

Explanation:

Desmond has a budget of $250

He has workers (Andrea and Max)

He wishes to pay Andrea $5 more than he pays Max per hour.

He makes Andrea work 10 hours and Max 15 hours.

Now we are told to create a system of equations that will help Desmond determine Andrea's hourly rate,a and Max's hourly rate,m

a-5 = m

10a+15m= 250

Substitute a-5=m in equation 2

10a+(15×a-5) = 250

10a+15a-75= 250

25a-75= 250

25a=250+75

25a=325

a=325/25

a= 13

Now substitute a= 13 in equation 1

13-5= 8

So Andrea's hourly rate is $13 and Max's hourly rate is $8

Answer 2

The system of equation is given by:

a - m = 5

10*a + 15*m = 250

And the solution gives us a = 13 and m = 8.

Explanation:

Desmond wants to pay 5$ more per hour Andrea than he pays Max. From that statement we can create one equation, that represents the difference between Max and Desmond payments, wich goes by:

a = m + 5

Desmond needs to fit the payment of his employees within a budget of $ 250, and he wants Andrea to work 10 hours while Max works for 15 hours. So the sum amount of time each employee works multiplied by the price of each hour should be equal to his budget. We have:

10*a + 15*m = 250

We have two equations and two variables, we can create a system that goes by:

a - m = 5

10*a + 15m = 250

In order to solve the system we can swap the value of a = m+ 5 into the second equation and solve for m, we have:

10(m+5) + 15m = 250

10m + 50 + 15m = 250

25m = 200

m = 8

In order to find the value of a, we put this value on the first equation:

a = m+5 = 8+5 = 13