SOLUTION: If two numbers are both increased by 10, their product is increased by 550. If twice the smaller number exceeds the larger by 15, find the numbers.

Question 225263: If two numbers are both increased by 10, their product is increased 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!
Two numbers, x & y
:
write an equation for each statement:
:
If two numbers are both increased by 10, their product is increased by 550.
New no. product - original product = 550
(x+10)*(y+10) - xy = 550
FOIL
xy + 10x + 10y + 100 - xy = 550
xy's cancel
10x + 10y + 100 = 550
10x + 10y = 550 - 100
10x + 10y = 450
Simplify, divide by 10
x + y = 45
:
If twice the smaller number exceeds the larger by 15,
x = 2y - 15
:
find the numbers.
Replace x in the 1st equation with (2y-15)
(2y-15) + y = 45
2y + y = 45 + 15
3y = 60
y =
y = 20
:
Find x:
x = 2(20) - 15
x = 25
;
:
See if that works in the 1st statement
35*30 - 25*20 =
1050 = 500 = 550
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