Question

15. Alvin, Simon and Theodore do volunteer work at Adopt-a-Pet Animal Shelter. They worked a total of 284 hours at the shelter last summer. Alvin worked 15 hours more than Simon. Theodore
worked 6 less than three times as many hours as Simon.
Write and solve an equation that expresses the relationship between the number of hours each person worked last summer and the total number of hours worked. Define the variable used in
your equation. SHOW ALL WORK!!!!
How many hours did each person work?

Answer 1

Answer: Hope this helps ;)

Step-by-step explanation:

Let's define the variables as follows:

A = number of hours Alvin worked

S = number of hours Simon worked

T = number of hours Theodore worked

We know that the total number of hours worked is the sum of the number of hours each person worked, so we can write the equation:

A + S + T = 284

We also know that Alvin worked 15 hours more than Simon, so we can write the equation:

A = S + 15

Finally, we know that Theodore worked 6 less than three times as many hours as Simon, so we can write the equation:

T = 3S - 6

We can substitute the second equation into the first equation to eliminate one of the variables:

(S + 15) + S + (3S - 6) = 284

This simplifies to:

5S = 263

Solving for S, we find that Simon worked 52.6 hours.

Substituting this value back into the equation A = S + 15, we find that Alvin worked 67.6 hours.

Finally, substituting the value of S into the equation T = 3S - 6, we find that Theodore worked 156.8 hours.

Therefore, Alvin worked 67.6 hours, Simon worked 52.6 hours, and Theodore worked 156.8 hours.