SOLUTION: Eight years ago, Albert was 3/4 of Bilbos age. in 22 years he will be 9/10 of Bilbos age. How old is Bilbo now?

Question 554120: Eight years ago, Albert was 3/4 of Bilbos age. in 22 years he will be 9/10 of Bilbos age. How old is Bilbo now?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Eight years ago, Albert was 3/4 of Bilbos age.
in 22 years he will be 9/10 of Bilbos age.
How old is Bilbo now?
:
Let a = Al's present age
Let b = Bil's
:
"Eight years ago, Albert was 3/4 of Bilbos age."
a - 8 = (b-8)
multiply both sides by 4
4(a-8) = 3(b-8)
4a - 32 = 3b - 24
4a = 3b - 24 + 32
4a = 3b + 8
divide both sides by 4
a = .75b + 2
:
"in 22 years he will be 9/10 of Bilbos age. "
a + 22 = (b+22)
multiply both sides by 10
10(a + 22) = 9(b + 22)
10a + 220 = 9b + 198
10a = 9b + 198 - 220
10a = 9b - 22
Replace a with (.75b+2)
10(.75b + 2) = 9b - 22
7.5b + 20 = 9b - 22
20 + 22 = 9b - 7.5b
42 = 1.5b
b = 42/1.5
b = 28 is Bil's age
:
:
:
Find a, then check the solutions in both statements:
a = .75(28) + 2
a = 23 is Al's age

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