SOLUTION: the sum of two numbers is 181. three times the larger number plus twice the smaller number is 459. find the number

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Question 204315: the sum of two numbers is 181. three times the larger number plus twice the smaller number is 459. find the number
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let a be the smaller number and b be the larger number.
1) a%2Bb+=+181 "The sum of two numbers is 181."
2) 2a%2B3b+=+459 "Three times the larger number (3b) plus twice the smaller number (2a) is 459.
Rewrite equation 1) as a+=+181-b and substitute into equation 2).
2a) 2%28181-b%29%2B3b+=+459 Expand the left side.
2a) %28362-2b%29%2B3b+=+459 Combine like-terms.
2a) 362%2Bb+=+459 Subtract 362 from both sides.
2a) highlight%28b+=+97%29 and
a+=+181-b
a+=+181-97
highlight_green%28a+=+84%29