Question

Four friends are playing a "Guess my Age" game. The come up with the following

clues. Dave's age is 15% of Sabrina. Luca's age is 75% of Sabrina and Rhianna is 300%
of Dave. The sum of their ages is 141. How old is Rhianna?
Show your work!

Answer 1

27 years old

Explanation:

What I know

Let D = Dave, S = Sabrina, etc. Then:

(1)
`D=0.15S`

(2)
`L=0.75S`

(3)
`R=3.00D`

(4)
`D+S+L+R=141`

Want to find R. Taking equation 3 and rewriting equation 4, we get

`R=3.00D`

`R=141-D-S-L`

So if
`R=R`, then

`3D=141-D-S-L-R`

`4D=141-S-L` by adding
`D` to both sides.

Using equation 1 and equation 2, I can rewrite everything in terms of
`S` and get:

`4(0.15S)=141-S-0.75S`

`0.6S=141-1.75S`

`2.35S=141` by adding
`1.75S` to both sides.

`S=60` by dividing 2.35 both sides.

Now that I know Sabrina's age, I'll work towards getting Rhianna's using equation 1 and equation 3:

`D=0.15(60)=9`

`R=3.00(9)=27`

Checking my work:

Dave: 9

Sabrina: 60

Luca: 45 (since 9+60+45+27=141)

Rhianna: 27

9 is 15% of 60

45 is 75% of 60

27 is 300% of 9