SOLUTION: Story Problem: One number is 2 more than 5 times the other. Their product is 24. These are the formulas that I came up with for this story problem, but after substitution metho

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Question 507830: Story Problem: One number is 2 more than 5 times the other. Their product is 24.
These are the formulas that I came up with for this story problem, but after substitution method I get the polynomial and get stumped on how to solve them.
xy=24
x=2+5y
(2+5y)y=24 5y^2 +2y=24 where do I go from here?
Found 2 solutions by Earlsdon, oberobic:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You're OK so far:
5y%5E2%2B2y+=+24 Subtract 24 from both sides.
5y%5E2%2B2y-24+=+0 Now you have a quadratic equation which you can solve using the quadratic formula: y+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a and here...a=5, b=2, and c=-24. Make the appropriate substitutions:
y+=+%28-2%2B-sqrt%282%5E2-4%285%29%28-24%29%29%29%2F2%285%29 Evaluate:
y+=+%28-2%2B-sqrt%284-%28-480%29%29%29%2F10
y+=+%28-2%2B-sqrt%28484%29%29%2F10
y%5B1%5D+=+-0.2%2B2.2 or y%5B2%5D+=+-0.2-2.2
y%5B1%5D+=+2 or y%5B2%5D+=+-2.4
x%5B1%5D+=+2%2B5y
x%5B1%5D+=+2%2B5%282%29
x%5B1%5D+=+12 or
x%5B2%5D+=+2%2B5%28-2.4%29
x%5B2%5D+=+2%2B%28-12%29
x%5B2%5D+=+-10
So there are two pairs of numbers that will satisfy the given constraints:
2 and 12
-2.4 and -10

Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
x * y = 24
so
x = 24/y
.
x = 5y + 2
.
x=x
so
24/y = 5y + 2
.
cross multiply
.
24 = y(5y + 2)
24 = 5y^2 + 2y
.
5y^2 +2y - 24 = 0
.
factor
.
(5y +12)(y - 2) = 0
.
check the factoring with FOIL
.
5y^2 -10y +12y -24.
OK
.
So, y = -12/5 or 2
.
substitute to find x
.
x*y = 24
x*2 = 24
x = 12
OK
.
x*y = 24
x*-12/5 = 24
x = -10
OK
.
x = -10 when y = -12/5
x = 12 when y = 2
.
Also check the other equation.
.
One number is 2 more than 5 times the other.
.
y = -12/5
x = 5y -2
x = 5*(-12/5) + 2
x = -12 + 2
x = -10
OK
.
y = 2
x = 5y +2
x = 10 + 2
x = 12
OK
.
So, we have two answers as shown above.
.
x = -10 when y = -12/5
x = 12 when y = 2
.
These could be shown as ordered pairs: (-10,-12/5), (12,2)
which suggests a graph.
.
x*y = 24
y = 24/x (red line in the following graph)
.
x = 5y + 2
5y = x -2
y = (1/5)x - 2/5 (blue line in the following graph)
.
graph%28500%2C500%2C-20%2C20%2C-20%2C20%2C24%2Fx%2C+1%2F5%2Ax+-+2%2F5%29