SOLUTION: One number is 40 more than twice another. Their product is 40 more than twice their sum. Find the numbers.

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Question 990080: One number is 40 more than twice another. Their product is 40 more than twice their sum. Find the numbers.
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
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x=one number; y=other number
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x=2y+40
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xy=2%28x%2By%29%2B40
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%282y%2B40%29%28y%29=2x%2B2y%2B40
2y%5E2%2B40y=2%282y%2B40%29%2B2y%2B40
2y%5E2%2B40y=4y%2B80%2B2y%2B40
2y%5E2%2B40y=6y%2B120
2y%5E2%2B34y-120=0
y%5E2%2B17y-60=0
%28y%2B20%29%28y-3%29=0
y%2B20=0 OR y-3=0
y=-20 OR y=3
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If y=-20:
x=2y+40
x=2(-20)+40
x=-40+40
x=0
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Solution 1: (0,-20)
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CHECK:
xy=2%28x%2By%29%2B40
%280%29%28-20%29=2%280%2B%28-20%29%29%2B40
0=-40%2B40
0=0
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If y=3:
x=2y+40
x=2(3)+40
x=6+40
x=46
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Solution 2: (46,3)
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CHECK:
xy=2%28x%2By%29%2B40
%2846%29%283%29=2%2846%2B3%29%2B40
138=2%2849%29%2B40
138=98%2B40
138=138
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ANSWER: The numbers are 0 and -20, or 46 and 3.