SOLUTION: class a and class b donated their class fund totaling $ 127 to an orphanage. if the amount donated by class a is $7 short of two-third of the amount donated by class b, how much mo

Question 242953: class a and class b donated their class fund totaling $ 127 to an orphanage. if the amount donated by class a is $7 short of two-third of the amount donated by class b, how much money was donated by each class ?
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
First we lay out the problem from what is given:
a = amount contributed by class 'a'
b = amount contributed by class 'b'
a + b = 127
We also are told that 2/3b is $7 more than a. We can adjust by adding $7 to 'a' or subtracting $7 from 2/3b. I'll do the latter.
a = 2/3b - 7
The original equation is: a+b=127. But we know that 2/3b is $7 more than the value 'a' ought to be, so subtract 7 from both sides:
2/3b + b = 120
Multiply both sides by 3 to remove the fraction and then collect terms:
3(2/3b + b) = 3(120)
2b + 3b = 360
5b = 360
Now divide both sides by 5:
b = 72
Now recall that a+b=127, so we can solve for a:
a = 127 - 72 = 55
We have our answer:
a = 55
b = 72
But we need to check our work!
Does a+b = 127? 55+27=127. Yes it does.
What is 2/3 of b?
2/3b = 48
Is $48 really $7 short of 55? Yes.
Done.
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