Question

"Alexis, Becca, and Cindy do volunteer work at Adopt-a-Pet Animal Shelter. They worked a total of 285 hours at the shelter last summer. Alexis worked 15 hours less than Becca. Cindy worked 4 more than twice as many hours as Becca."

show all work

Answer 1

Alexis = 59

Becca = 74

Cindy = 152

Explanation:

a + b + c = 285

a = b - 15

c = 2b + 4

Answer 2

Alexis worked 59 hours, Cindy worked 152 hours and Becca worked 74 hours.

Explanation:

Givens

• They worked a total of 285 hours.
• Alexis worked 15 hours less than Becca.
• Cindy worked 4 more than twice as many hours as Becca.
• Alexis is
  `A`.
• Cindy is
  `C`
• Becca is
  `B`

The expressions that model this problem would be

`A+C+B=285`

Because all together they work 285 hours.

`A=B-15`

Because Alexis worked 15 hours less than Becca.

`C=4+2B`

Because Cindy worked 4 hours more than twice Becca's hours

Now, we replace the last two expression in the first one

`B-15+4+2B+B=285\\4B-11=285\\4B=285+11\\B=(296)/(4)=74`

Then, we replace this value to find others

`C=4+2B=4+2(74)=152`

`A=B-15=74-15=59`

Therefore, Alexis worked 59 hours, Cindy worked 152 hours and Becca worked 74 hours.