SOLUTION: Divide 556 into two parts such that if the larger part is added to 12 and the smaller part is added to 18 the resulting sums would be equal.

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Question 169240: Divide 556 into two parts such that if the larger part is added to 12 and the smaller part is added to 18 the resulting sums would be equal.
Answer by nerdybill(7384) About Me  (Show Source):
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Divide 556 into two parts such that if the larger part is added to 12 and the smaller part is added to 18 the resulting sums would be equal.
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Let L = larger part
and S = smaller part
.
Since we have two unknowns, we'll need two equations:
L + S = 556 (equation 1)
L + 12 = S + 18 (equation 2)
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Solving equation 1 for S:
L + S = 556
S = 556 - L
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Plug the above into equation 2 and solve for L:
L + 12 = S + 18
L + 12 = 556 - L + 18
L + 12 = 574 - L
2L + 12 = 574
2L = 562
L = 281 (larger number)
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To find the smaller number, plug the above into equation 1:
L + S = 556
281 + S = 556
S = 556 - 281
S = 275 (smaller number)