SOLUTION: The product of two numbers is 1400. If three is subtracted from each number, their product becomes 1175. Find the bigger number.

Question 697366:
The product of two numbers is 1400. If three is subtracted from each number, their product becomes 1175. Find the bigger number.
Found 2 solutions by nerdybill, checkley79:
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
The product of two numbers is 1400. If three is subtracted from each number, their product becomes 1175. Find the bigger number.
.
Let x = one number
and y = second number
.
From: "The product of two numbers is 1400."
xy = 1400 (equation 1)
.
From: "If three is subtracted from each number, their product becomes 1175."
(x-3)(y-3) = 1175 (equation 2)
.
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}
.
Answer: 50

Answer by checkley79(3341) (Show Source): You can put this solution on YOUR website!
XY=1400
X=1400/Y
(X-3)(Y-3)=1175
XY-3Y-3X+9=1175
1400-3Y=3(1400/Y)=1175-9
1400-3Y=4200/Y=1166
-3Y-4200/Y=1166-1400
(-3Y*Y-4200)/Y=-234
-3Y^2-4200=-234Y
-3Y^2+234Y-4200=0
3Y^2-234Y+4200=0
3(Y^2-78Y+1400=0
3(Y-50)(Y-28)=1400
Y-50=0
Y=50 ANS. THEN X*50=1400 OR X=1400/50 OR X=28 ANS.
Y-28=0
Y=28 ANS. THEN X*28=1400 OR X=1400/28 OR X=50 ANS.
PROOF:
50*28=1400
1400=1400
(28-3)(50-3)=1175
25*47=1175
1175=1175
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