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!

Answers

Answer 1

Answer:

27 years old

Step-by-step explanation:

What I know

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

(1) [tex]D=0.15S[/tex]

(2) [tex]L=0.75S[/tex]

(3) [tex]R=3.00D[/tex]

(4) [tex]D+S+L+R=141[/tex]

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

[tex]R=3.00D[/tex]

[tex]R=141-D-S-L[/tex]

So if [tex]R=R[/tex], then

[tex]3D=141-D-S-L-R[/tex]

[tex]4D=141-S-L[/tex] by adding [tex]D[/tex] to both sides.

Using equation 1 and equation 2, I can rewrite everything in terms of [tex]S[/tex] and get:

[tex]4(0.15S)=141-S-0.75S[/tex]

[tex]0.6S=141-1.75S[/tex]

[tex]2.35S=141[/tex] by adding [tex]1.75S[/tex] to both sides.

[tex]S=60[/tex] 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:

[tex]D=0.15(60)=9[/tex]

[tex]R=3.00(9)=27[/tex]

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


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