Question 697366
    The product of two numbers is 1400. If three is subtracted from each number, their product becomes 1175. Find the bigger number.
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Let x = one number
and y = second number
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From: "The product of two numbers is 1400."
xy = 1400 (equation 1)
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From: "If three is subtracted from each number, their product becomes 1175."
(x-3)(y-3) = 1175 (equation 2)
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solve equation 1 for x:
xy = 1400
x = 1400/y
substitute above into equation 2 and solve for y:
(x-3)(y-3) = 1175
(1400/y-3)(y-3) = 1175
multiplying both sides by y:
(1400-3y)(y-3) = 1175y
1400y-4200-3y^2+9y = 1175y
1409y-4200-3y^2 = 1175y
-3y^2+1409y-4200 = 1175y
-3y^2+234y-4200 = 0
3y^2-234y+4200 = 0
y^2-78y+1400 = 0
(y-28)(y-50) = 0
y = {28, 50}
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Answer: 50