Question

Mac's Grocery has 25 employees. The average daily wage for a teen is $52, and the average daily wage for an adult is $90. If the daily payroll is $1,984, how many teens and how many adults are employed?

Answer 1

These questions used to make me cry.

18 adults, 7 teens
——————-

We’ll call a the number of adult employees, and t the number of teen employees.

We know a + t = 25
We also know 90a + 52t = 1984
(The amount paid to adults times the number of adults plus the amount paid to teens times the number of teens = weekly payroll.)

a + t = 25
90a + 52t = 1984

We’ll solve for a in terms of t
a = 25 - t
Then substitute that into the other equation. Then we can get a numerical value for t.

90(25-t) + 52t = 1984
2250 - 90t + 52t = 1984
266 = 38t
t = 7

Then we substitute that into our first equation to solve for a

a + 7 = 25
a = 18

Checking the math:
90(18) + 52(7) = 1620 + 364 = 1984

Let me know if you have questions.

Answer 2

The answer would be 18 adults and 7 teens. 90 times 18 equals 1,620 and 52 times 7 equals 364. 1,620+364=1,984.