SOLUTION: find two numbers such that five times the larger plus three times the smaller is 47,and four times the larger minus twice the smaller is 20.

Question 165144: find two numbers such that five times the larger plus three times the smaller is 47,and four times the larger minus twice the smaller is 20.
Answer by orca(409) (Show Source): You can put this solution on YOUR website!
Let x and y be the larger and smaller numbers respectively.
Use the given fact "five times the larger plus three times the smaller is 47" to set up an equation:
5x + 3y = 47 ...................(1)
Use the given fact "four times the larger minus twice the smaller is 20" to set up another equation:
4x - 2y = 20 ...................(2)
Multiply both sides of (1) by 2, we have:
10x + 6y = 94 ............................(3)
Multiply both sides of (2) by 3, we have:
12x - 6y = 60 ............................(4)
Add (3) and (4), we have
22x = 154
x = 7
Substituting x = 7 into (1), we have
5*7 + 3y = 47
Solving for y, we have:
35 + 3y = 47
3y = 12
y = 4

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