SOLUTION: when 4 times the larger of two numbers is added to 3 times the smaller, the result is 68. seven times the larger less 5 times is 37. find the number

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Question 160022: when 4 times the larger of two numbers is added to 3 times the smaller, the result is 68. seven times the larger less 5 times is 37. find the number
Found 2 solutions by Fombitz, checkley77:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let's call the larger number L and the smaller one S.
1.4L%2B3S=68
2.7L-5S=37
Use eq. 1 to solve for L in terms of S.
1.4L%2B3S=68
4L=68-3S
L=17-%283%2F4%29S
Now substitute this expression for L into eq. 2 and solve for S.
2.7L-5S=37
7%2817-%283%2F4%29S%29-5S=37
7%2817-%283%2F4%29S%29-5S=37
119-%2821%2F4%29S-5S=37
-%2821%2F4%29S-%2820%2F4%29S=-82
-%2841%2F4%29S=-82
S=%2882%2A4%29%2F41
highlight%28S+=8%29
From eq. 1,
L=17-%283%2F4%29S
L=17-%283%2F4%298
L=17-6
highlight%28L=11%29

Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
4Y+3X=68
7Y-5X=37(?)
MULTIPLY THE FIRST EQUATION BY 5 & MULTIPLYTHE SECOND EQUATION BY 3 & ADD THEM.
20Y+15X=340
21Y-15X=111
-----------------
41Y=451
Y=451/41
Y=11 ANSWER FOR THE LARGER NUMBER.
4*11+3X=68
44+3X=68
3X=68-44
3X=24
X=24/3
X=8 ANSWER FOR THE SMALLER NUMBER.
PROOF:
7*11-5*8=37
77-40=37
37=37