SOLUTION: Three times the larger of two numbers is equal to four times the smaller. The sum of the numbers is 21. Find the numbers

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Question 907509: Three times the larger of two numbers is equal to four times the smaller. The sum of the numbers is 21. Find the numbers
Answer by AlgebraLady88(44) About Me  (Show Source):
You can put this solution on YOUR website!
We will call the larger of two numbers L and the smaller of the numbers S.
Three times the larger of two numbers is equal to four times the smaller.
This can be written as
3L=4S
The sum of the numbers is 21.
This can be written as L+S= 21
We can plug the equation L+S =21 into 3L=4S either using L= 21-S or S= 21-L.
Let's try L= 21-S
3L=4S
3(21-S)= 4S
63 -3S = 4S
-3S-4S = -63
-7S = -63
7S = 63
S = 9
If S=9, then 3L=4S
3L= 4(9)
3L= 36
L= 12
Check our work
3L= 4S
3(12) = 4 (9) Yes!