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Question 165142: find two numbers such that five times the larger plud three times the smaller is 47 and four times the larger minus twice the smaller is 20.
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! Let S = smaller number
and
L = larger number
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Since we have two unknowns, we'll need two equations.
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Equation 1: "five times the larger plus three times the smaller is 47"
5L + 3S = 47
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Equation 2: "four times the larger minus twice the smaller is 20"
4L - 2S = 20
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Using the "substitution method", solve equation 2 for S:
4L - 2S = 20
4L = 2S + 20
4L-20 = 2S
2L-10 = S
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Substitute the above into equation 1 and solve for L:
5L + 3S = 47
5L + 3(2L-10) = 47
5L + 6L-30 = 47
11L - 30 = 47
11L = 77
L = 7
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Finally, plug the above back into equation 2 and solve for S:
4L - 2S = 2
4(7) - 2S = 2
28 - S = 1
28 = S + 1
27 = S
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Solution: The two numbers are 7 and 27
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