Therefore, Bill and Gina would have the same number of coins, 80 each.

Therefore, In summary, there is not enough information to answer the question of who has more coins, as there are an infinite number of possible solutions to the given equation. To find a specific answer, there needs to be 2 equations with 2 variables.
  • #1
Spirochete
127
0

Homework Statement


The number of coins in Bill's collection is 80 less than twice the number in Gina's collection.

Who has more coins?

The answer is "Not enough information to answer the question."

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?
 
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  • #2
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
Spirochete said:

Homework Statement


The number of coins in Bill's collection is 80 less than twice the number in Gina's collection.

Who has more coins?

The answer is "Not enough information to answer the question."

The Attempt at a Solution



The way you do these problems is figure out the equation then plug in different numbers.
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.
Spirochete said:
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?

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
B+80=2G

Is that right?
 
  • #5
Spirochete said:
B+80=2G

Is that right?

Yes, that's correct.
 
Last edited:
  • #6
Now that you have an equation, can you answer the question: who has more coins?
 
  • #7
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
This creates an equation with 2 variables.
[tex]B+80=2G[/tex]

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

Therefore, [tex]y=2x-80[/tex]
As you can see if you plotted the graph that any [tex]x\geq 40[/tex] 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: [tex]100-G=\frac{B}{4}[/tex]

Therefore, [tex]y=-4x+400[/tex]

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:

What is a GRE algebra word problem?

A GRE algebra word problem is a type of mathematical problem that appears on the Graduate Record Examination (GRE) test. It involves using algebraic equations and solving for an unknown variable based on given information in the form of words or phrases.

Are GRE algebra word problems difficult?

It depends on the individual's math skills and preparation for the GRE. Some people may find them challenging while others may find them manageable. It is important to practice and familiarize oneself with different types of GRE algebra word problems to improve performance.

How can I solve a GRE algebra word problem?

The key to solving GRE algebra word problems is to carefully read and identify important information, translate the words into mathematical equations, and then solve for the unknown variable using algebraic techniques such as factoring, substitution, or elimination.

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Yes, it is important to show your work when solving GRE algebra word problems. The GRE test typically requires students to show their work and explain their reasoning in order to receive full credit for their answers.

What are some tips for improving my performance on GRE algebra word problems?

Practice regularly with different types of GRE algebra word problems, review algebraic concepts and techniques, and carefully read and analyze the given information before attempting to solve the problem. Additionally, it can be helpful to work backwards from the answer choices to check your work and eliminate incorrect options.

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