SOLUTION: The sum of two numbers is 35. If the larger is doubled and the smaller is tripled,the difference is 5.find the numbers?

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Question 1057966: The sum of two numbers is 35. If the larger is doubled and the smaller is tripled,the difference is 5.find the numbers?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Two numbers a & b
:
Write an equation for each statement
:
The sum of two numbers is 35.
a + b = 35
a = 35 - b; use this form for substitution
:
If the larger is doubled and the smaller is tripled, the difference is 5.
2a - 3b = 5
Replace a with (35-b)
2(35 - b) - 3b = 5
70 - 2b - 3b = 5
-5b = 5 - 70
-5b = -65
b = -65/-5
b = +13
then
a = 35 - 13
a = 22
:
See if that checks out in the 2nd equation
2(22) - 3(13) =
44 - 39 = 0
:
find the numbers? 22 & 13