Question 548889: There are two numbers. the second number is 3 more than the first.the prouduct of the two numbers ia 9 more than teir sum. What are the two numbers?
Answer by Maths68(1474)   (Show Source):
You can put this solution on YOUR website! Let y and x be the first and second numbers
The second number is 3 more than the first
x=y+3..........(1)
The product of the two numbers is 9 more than their sum
xy=(x+y)+9......(2)
Put the value of x from (1) to (2)
(y+3)y=(y+3)+y)+9
y^2+3y=y+3+y+9
y^2+3y=2y+12
y^2+3y-2y-12=0
y^2+y-12=0
y^2+4y-3y-12=0
y^2+4y-3y-12=0
y(y+4)-3(y-4)=0
(y+4)(y-3)=0
y+4=0 or y-3=0
y=-4 or y=3
Put y=3 in (1)
x=y+3..........(1)
y=3
x=3+3
x=6
Put y=-4 in (1)
x=(-4)+3
x=-4+3
x=-1
x,y=6,3 or x,y=-1,-4
Check
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Put x,y=(6,3) in (1)
x=y+3..........(1)
6=3+3
6=6
Put x,y=(6,3) in (2)
xy=(x+y)+9......(2)
(6)(3)=(6+3)+9
18=9+9
18=18
Put x,y=(-1,-4) in (1)
x=y+3..........(1)
-1=-4+3..........(1)
-1=-1
Put x,y=(-1,-4) in (2)
xy=(x+y)+9......(2)
(-1)(-4)=(-1-4)+9
4=-5+9
4=4
Numbers are = 3,6 or -4,-1
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