Reverse factoring

[cmr209]

Ok, I'm getting frustrated here.

So it has been said that the GMAT rewards for mental flexibility, yet I'm struggling with this reverse factoring.

Example:

Solve for "k" in terms of "m"

m - 3 = k/4

k = 4(m - 3) = 4m - 12.

Using the foil method I see how that is the answer, however, How do not understand how I get to the first step of breaking apart the fraction k/4 to mean k = 4(m - 3)?

This is how I approached the problem on my first attempt:

m - 3 = k/4

m = k/4 + 3

m = k/4 + 3/1

m = k/4 + 12/4

m = k12/4

m = k3

What am I doing wrong?
Please advise.

[bharathh]

Ok, I'm getting frustrated here.

So it has been said that the GMAT rewards for mental flexibility, yet I'm struggling with this reverse factoring.

Example:

Solve for "k" in terms of "m"

m - 3 = k/4

k = 4(m - 3) = 4m - 12.

Using the foil method I see how that is the answer, however, How do not understand how I get to the first step of breaking apart the fraction k/4 to mean k = 4(m - 3)?

This is how I approached the problem on my first attempt:

m - 3 = k/4

m = k/4 + 3

m = k/4 + 3/1

m = k/4 + 12/4
m = k12/4

m = k3


What am I doing wrong?
Please advise.

Marked in red.

You did fine until then.

Since you have a common denominator now. Add the two numerators. (k+12)/4 = m

[cmr209]

bharathh,

I don't see how that comes to = 4m - 12?

I redid the problem at m = k/4 + 12/4

m = k + 12
           4

m = k + 3

[bharathh]

Ok I just read what you were asking for in the post.

Solve for k in terms of m

So first up that means you need k = some eqn with m in it.

You are given m - 3 = k/4

There really is only step to this.

Multiply both sides by 4... When you perform a mathematical operation to both sides of the equation, you keep the equation unchanged.

So 4*(m-3) = 4*k/4

The four multiplied to k/4 makes it k

so you are left with k = 4(m-3)

now solve it using the FOIL method.

[bharathh]

Check out this site. I would highly recommend you go through this before attempting any GMAT questions

https://serc.carleton.edu/mathyouneed/Equation.html

[cmr209]

Nice!!

Thank you!

I now see I have to remember the basic step of when I'm trying to get rid of a division I can multiply the denominator by the other side. You've helped me realize my mistake!

Again, thank you!

[grockit_jake]

m = (k + 12) / 4

4m = k + 3

You have to remember to multiply left AND right by the exact same thing. Also, when you have an addition on the top dividing a term on the bottom, you can split it up but you can't divide only 1 of the terms.