Question

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?

Again, SHOW ALL WORK!!!!

Answer 1

Therefore, Alvin worked 70 hours, Simon worked 55 hours, and Theodore worked 159 hours

Explanation:

Let A be the number of hours Alvin worked, S be the number of hours Simon worked, and T be the number of hours Theodore worked.
We know that the total number of hours worked is the sum of the hours each person worked, so we can write the equation:A + S + T = 284
We also know that Alvin worked 15 more hours than Simon, so we can write the equation:A = S + 15
We also know that Theodore worked 6 less than three times as many hours as Simon, so we can write the equation:T = 3S - 6
Substituting the second equation into the first equation, we get:
S + S + 15 + 3S - 6 = 284
Combining like terms, we get:5S + 9 = 284
Subtracting 9 from both sides, we get:5S = 275
Dividing both sides by 5, we get:S = 55
Substituting this value into the equation A = S + 15, we get:
A = 55 + 15A = 70
Substituting this value into the equation T = 3S - 6, we get:T = 3 * 55 - 6T = 165 - 6T = 159