SOLUTION: please help me to solve this: If two numbers are both increase by ten there product is increase by 550. if twice the smaller number exceeds the larger by 15, find the numbers.

Question 123584: please help me to solve this:
If two numbers are both increase by ten there product is increase by 550. if twice the smaller number exceeds the larger by 15, find the numbers.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Let x = a number; y = a smaller number
:
Write an equation for each statement:
:
"If two numbers are both increased by ten their product is increased by 550"
(x + 10) * (y + 10) = (x*y) + 550
:
"twice the smaller number exceeds the larger by 15,"
2y = x + 15
or
x = (2y - 15)
:
Substitute this for x in the 1st equation:
((2y-15) + 10) * (y + 10) = y(2y-15) + 550
:
(2y - 5) * (y + 10) = 2y^2 - 15y + 550
FOIL
2y^2 + 20y - 5y - 50 = 2y^2 - 15y + 550
:
Arrange the y's on the left and numerical values on the right
:
2y^2 - 2y^2 + 15y + 15y = 550 + 50; the two 2y^2's conveniently cancl
:
30y = 600
y =
y = 20
:
Find x using x = 2y - 15
x = 2(20) - 15
x = 25
:
:
Check solution, new numbers are 35 & 30
35 * 30 = 1050
25 * 20 = 500
--------------
differ = 550
:
Did this make logical sense?

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