SOLUTION: bianca is twice as old as pio and margie as twice as old as bianca. In 10 years, their combined ages is 58.How old is bianca now?

Question 1014312: bianca is twice as old as pio and margie as twice as old as bianca. In 10 years, their combined ages is 58.How old is bianca now?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let b = bianca's age now.
let p = pio'a age now.
let m = margie's age now.

in 10 years the sum of their ages will be 58.

this means that:

b + 10 + p + 10 + m + 10 = 58

combine like terms and you get b + p + m + 30 = 58

subtract 30 from both sides of this equation to get b + p + m = 28

you are given that bianca is twice as old as pio and margie is twice as old as bianca.

this leads to:

b = 2p
m = 2b
p = p

since m = 2b and b = 2p, then m = 2 * (2p) = 4p

your relationships between their ages now becomes:

b = 2p
m = 4p
p = p

now that all the ages are in relationship to pio's age, you can solve.

you have b + p + m = 28

replace b with 2p and replace m with 4p and you get 2p + p + 4p = 28.

combine like terms to get 7p = 28

solve for p to get p = 4.

when p = 4, 2p = 8 and 4p = 16

bianca is 8 years old.
pio is 4 years old.
margie is 16 years old.

bianca is twice as old as pio
8/4 = 2
this checks out.

margie is twice as old as bianca
16/8 = 2
this check out.

8 + 4 + 16 = 28.
this checks out.

in 10 years, bianca will be 18 and pio will be 14 and margie will be 26.
18 + 14 + 26 = 58
this checks out.

everything checks out.
your solution is that bianca is 8 years old now.

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