SOLUTION: There is only 12 years difference between Amy and Billy’s ages yet 30 years ago billy was twice Amy’s age what are billy and Amy’s ages now
Algebra ->
Customizable Word Problem Solvers
-> Age
-> SOLUTION: There is only 12 years difference between Amy and Billy’s ages yet 30 years ago billy was twice Amy’s age what are billy and Amy’s ages now
Log On
Question 1141697: There is only 12 years difference between Amy and Billy’s ages yet 30 years ago billy was twice Amy’s age what are billy and Amy’s ages now Found 3 solutions by ankor@dixie-net.com, greenestamps, josgarithmetic:Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! a = Amy's present age
b = Billy's
:
There is only 12 years difference between Amy and Billy’s ages
a - b = 12
yet 30 years ago billy was twice Amy’s age
a - 30 = 2(b-30)
a - 30 = 2b - 60
a = 2b - 60 + 30
a = 2b - 30
:
in the first equation, replace a with (2b-30)
2b - 30 - b = 12
2b - b = 12 + 30
b = 42 is billy's age
and
12 + 42 = 54 is Amy's age
:
:
Check solutions in the statement
" 30 years ago billy was twice Amy’s age"
54 - 30 = 2(42-30)
24 = 12(12)
If a formal algebraic solution is not required, you can get some good mental exercise solving the problem using logical reasoning (and it's a lot faster than the formal algebra!).
(1) If the difference in their ages is 12 years, then when Billy was twice as old as Amy their ages were 24 and 12.
(2) Since that was 30 years ago, their ages are now 54 and 42.
(