Question

In one month, Juan worked 5 more hours than Carlito. Sara worked 3 times as many hours as Juan. Altogether they worked 80 hours

Let C= Hours Carlito worked

Let J= Hours Juan worked

Let S= Hours Sara worked

Which equation would represent the fact that altogether they worked 80 hours?
Which equation would represent the fact that Juan worked 5 more hours than Carlito?
How many hours did Sara work?

Answer 1

Explanation:

Let C represent the number of hours that Carlito worked.

Let J represent the number of hours that Juan worked.

Let S represent the number of hours that Sara worked.

1) The equation that would represent the fact that altogether they worked 80 hours is

C + J + S = 80

2) The equation that would represent the fact that Juan worked 5 more hours than Carlito is

J = C + 5

3) Sara worked 3 times as many hours as Juan. It means that

S = 3J

Substituting J = C + 5 into S = 3J, it becomes

S = 3(C + 5)

S = 3C + 15

Substituting S = 3C + 15 and

J = C + 5 into C + J + S = 80, it becomes

C + C + 5 + 3C + 15 = 80

C + C + 3C + 5 + 15 = 80

5C + 20 = 80

5C = 80 - 20

5C = 60

C = 60/5

C = 12

S = 3C + 15 = 3 × 12 + 15

S = 51 hours

Sara worked for 51 hours

Answer 2

The answer to your question is a) C + J + S = 80

b) C = J + 5

c) S = 45 hours

Explanation:

a) To represent the number of hours that they work together, just add the variables and equal them to 80.

Carlito + Juan + Sara = 80

C + J + S = 80 Equation l

b) Juan worked 5 hours more than Carlito

Juan = Carlito + 5

J = C + 5 Equation ll

c) Hours worked by Sara

S = 3J Equation lll

C = J - 5

Substitute equation ll and lll in equation l to find J

J - 5 + J + 3J = 80

5J = 80 - 5

5J = 75

J = 75/5

J = 15

-Find S

S = 3(15)

S = 45 hours