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Question 1085030: One number is 9 greater than another. The product of the numbers is 70. Find the numbers.
Answer by addingup(3677)   (Show Source):
You can put this solution on YOUR website! x = y+9
x × y = 70 substitute for x:
(y+9) × y = 70 now distribute the y (distributive properties of multiplication)
y^2+9y = 70
The coefficient of y is 9. Divide 9 by 2 and square it, then add to both sides of the equation:
y^2+9y+(9/2)^2 = 70+(9/2)^2
y^2+9y+81/4 = 70+81/4 solve the addition on the right: 70*4+81 = 361/4
y^2+9y+81/4 = 361/4 factor the left side. We have perfect squares so we can do it this way:
(y+9/2)^2 = 361/4 take the square root, both sides:
y+9/2 = 19/2 or y+9/2 = -19/2
y = 10/2 or y = -28/2
y = 5 or y = -14
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Let's see which one's your answer, we'll start with the 5:
5+9 = 14 and 5*14 = 70 so there you have it, 5 is your answer
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