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

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) (Show Source): You can put this solution on YOUR website!
Let's call the larger number L and the smaller one S.
1.
2.
Use eq. 1 to solve for L in terms of S.
1.

Now substitute this expression for L into eq. 2 and solve for S.
2.

From eq. 1,

Answer by checkley77(12844) (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

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