Question 283474: Find two numbers whose sum is 55 and product is 600.
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! "Two numbers" suggests we use 'x' and 'y'.
However, we are told they sum to 55: x + y = 55
That means we can substitute 55-x for y.
That, in turn, means we have only one unknown to solve.
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We also are told that x*y = 600
Substituting y = 55-x
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x*(55-x) = 600
55x -x^2 = 600
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Add x^2 to both sides
55x = x^2 + 600
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Subtract 55x from both sides
0 = x^2 -55x + 600
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Factor
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(x-15)(x-40)=0
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So we we have two possible values for x: 15 and 40.
That means we have two possible values for y:
55-15 = 40 and
55-40 = 15.
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Answer:
The two numbers are 15 and 40. Their sum is 55. Their product is 600.
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Done.
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