It's just been so long that I've done this, I dont remember how
How do you solve the following for Y?
1/2y(y+2)=24?
No matter what I do, I screw it up!!!
Very easy algebraic problem that I'm struggling with
This topic has expert replies
Ok..here is my take.
1/2Y(Y+2)=24
1) Notice the fraction...i always try to get rid of the fractions. So here i would multiply both sides of the equation by "2".
2 * 1/2Y(Y+2) = 24 * 2
2) The above step got rid of the 1/2, now solve for Y.
Y(Y+2)= 48
Multiply by Y
Y^2 + 2Y=48
Now subtract 48 from the right side and move to the left and set EQ to 0
Y^2 + 2Y - 48= 0
reverse FOIL
(Y-6) (Y+ 8 ) = 0
set Y-6=0 ---> Y=6
set Y+8=0 ---> Y=-8
So Y= 6 & -8
1/2Y(Y+2)=24
1) Notice the fraction...i always try to get rid of the fractions. So here i would multiply both sides of the equation by "2".
2 * 1/2Y(Y+2) = 24 * 2
2) The above step got rid of the 1/2, now solve for Y.
Y(Y+2)= 48
Multiply by Y
Y^2 + 2Y=48
Now subtract 48 from the right side and move to the left and set EQ to 0
Y^2 + 2Y - 48= 0
reverse FOIL
(Y-6) (Y+ 8 ) = 0
set Y-6=0 ---> Y=6
set Y+8=0 ---> Y=-8
So Y= 6 & -8
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Not sure if your problem should be read as:
(1/2y)(y+2)=24
or
(1/2)(y)(y+2) = 24
For the first version:
distribute the 1/2y to get: 1/2 + 1/y = 24
subtract the 1/2 to get: 1/y = 23.5
then take reciprocal of both sides to get: y = 1/23.5 = 2/47
For the second version:
multiply by 1/2 to remove fraction: y(y+2) = 48
distribute the left side: y^2 + 2y = 48
get everything on one side: y^2 + 2y - 48 = 0
factor: (y+8)(y-6) = 0
y = -8, y = 6
(1/2y)(y+2)=24
or
(1/2)(y)(y+2) = 24
For the first version:
distribute the 1/2y to get: 1/2 + 1/y = 24
subtract the 1/2 to get: 1/y = 23.5
then take reciprocal of both sides to get: y = 1/23.5 = 2/47
For the second version:
multiply by 1/2 to remove fraction: y(y+2) = 48
distribute the left side: y^2 + 2y = 48
get everything on one side: y^2 + 2y - 48 = 0
factor: (y+8)(y-6) = 0
y = -8, y = 6
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Stacey Koprince
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Stacey Koprince
GMAT Instructor
Director of Online Community
Manhattan GMAT
Contributor to Beat The GMAT!
Learn more about me