# GRE algebra word problem

1. Jan 20, 2009

### Spirochete

1. The problem statement, all variables and given/known data
The number of coins in Bill's collection is 80 less than twice the number in Gina's collection.

Who has more coins?

3. The attempt at a solution

The way you do these problems is figure out the equation then plug in different numbers. If you get two different answers it means the info you've been given is not enough to get an answer.

I just can't figure out how to make an equation. Could anybody explain in words how they come up with an equation to match that information?

2. Jan 20, 2009

### cristo

Staff Emeritus
The answer is 'not enough information' because you can only make one equation with two variables. To find this out, just translate the words into symbols. What do you get if you try and directly translate the sentence?

3. Jan 20, 2009

### Staff: Mentor

That's not the way to do these problems successfully. After you get your equation, you solve the equation for the variable you're interested in, not just plug random numbers into it.
Here's a start for you:
Let B = the number of coins in Bill's collection
Let G = the number of coins in Gina's collection

Now, can you translate this sentence into a mathematical equation, using the variables above?
"The number of coins in Bill's collection is 80 less than twice the number in Gina's collection."

4. Jan 20, 2009

### Spirochete

B+80=2G

Is that right?

5. Jan 20, 2009

### cristo

Staff Emeritus
Yes, that's correct.

Last edited: Jan 20, 2009
6. Jan 20, 2009

### Staff: Mentor

Now that you have an equation, can you answer the question: who has more coins?

7. Jan 20, 2009

### Spirochete

Well I don't see how I could figure it out without plugging in two very different numbers for Bill, and then solving for Gina. I tried Bill=One and then Bill=1000 and got two different answers, therefore the answer is "not enough info."

8. Jan 20, 2009

### Mentallic

This creates an equation with 2 variables.
$$B+80=2G$$

This is a linear equation. Let B=y and G=x

Therefore, $$y=2x-80$$
As you can see if you plotted the graph that any $$x\geq 40$$ corresponds with a different y value. In other words, as Bill's number of coins change, Gina's will change accordingly to satisfy this relationship. There are an infinite number of different possible solutions, and this is why there is not enough information to find a specific answer.

To solve for 2 variables, there needs to be 2 equations. So, say for e.g. there was also another set of criteria for this question. '100 coins minus Gina's coin collection is one fourth the size Bill's'

In equation form: $$100-G=\frac{B}{4}$$

Therefore, $$y=-4x+400$$

Now we have 2 equations with 2 variables. This is now solvable for 1 specific x value and its corresponding y value. Graphically, it would be the intersection of these 2 equations.

So, to satisfy these 2 equations, x=80 (Bill's collection) and correspondingly, y=80 (Gina's collection).

Last edited: Jan 20, 2009