SOLUTION: One number is 5 bigger than another number. When one third of the smaller number is added to half the bigger number the answer is 10. Find the smaller number

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: One number is 5 bigger than another number. When one third of the smaller number is added to half the bigger number the answer is 10. Find the smaller number       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1005246: One number is 5 bigger than another number. When one third of the smaller number is added to half the bigger number the answer is 10. Find the smaller number
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
One number is 5 bigger than another number.
When one third of the smaller number is added to half the bigger number the answer is 10.
Find the smaller number
:
Two numbers, a & b, b is the smaller
:
a = b + 5
and
1%2F3b + 1%2F2a = 10
multiply equation by the least common multiple of the denominators, 6
6*1%2F3b + 6*1%2F2a = 6(10)
Cancel the denominators
2b + 3a = 60
We know a = b+5
2b + 3(b+5) = 60
2b + 3b + 15 = 60
5b = 60 - 15
5b = 45
b = 45/5
b = 9 is the smaller number
:
:
a = 9 + 5 = 14
Confirm this in the statement,"When one third of the smaller number is added to half the bigger number the answer is 10."
1%2F3*9 + 1%2F2*14 = 10
3 + 7 = 10