Word Problem: Trouble transforming into mathematical equatio  TOPIC_SOLVED

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Word Problem: Trouble transforming into mathematical equatio

Postby jwroblewski44 on Mon Jun 03, 2013 1:58 am

Hello all! I am re-learning algebra from the ground up and am thankful I found this place for assistance. I have a word problem I am having trouble transforming into mathematical equations.

Here is the problem:
In Crystal’s silverware drawer there are twice as many spoons as forks. If Crystal adds nine forks to the drawer, there will be twice as many forks as spoons. How many forks and how many spoons are in the drawer right now?

I have been working on this for too long and need a little help. I have been jotting down some truth's such as

total = spoons + forks
spoons = 2 * forks

I'm quite stuck trying to fit the adding of nine forks and that switching of fork-to-spoon ratio in the equations.

Thanks in advance.
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Postby stapel_eliz on Mon Jun 03, 2013 2:41 am

jwroblewski44 wrote:In Crystal’s silverware drawer there are twice as many spoons as forks. If Crystal adds nine forks to the drawer, there will be twice as many forks as spoons. How many forks and how many spoons are in the drawer right now?

Let's pick some letters to stand for unknowns; I'll use "s" for the number of spoons and "f" for the number of forks.

In total, there are twice as many spoons as forks, so the number of spoons "s" is twice the number of forks "f". Translate "(spoons) is (twice)(forks)" into an equation.

If we add nine forks, then this will be twice as many forks as spoons. Translate "(forks) plus (another nine) is (twice)(spoons)" into an equation.

Then solve the system of equations! :wink:
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Re: Word Problem: Trouble transforming into mathematical equ  TOPIC_SOLVED

Postby jg.allinsymbols on Tue Jun 04, 2013 1:14 am

Assign some variables, and translate the descriptions directly into expressions or equations.

let s = number of spoons
let f = number of forks

"Twice as many spoons as forks", gives you s=2*f

If f+9 then f+9=2(s), or f+9=2*(2f), "add nine forks, then twice as many forks as spoons.

The system would seem to be s=2f AND f+9=4f, so you have one equation using only one unknown variable.

Forming that second equation seems somewhat confusing and my logic and intuition had to work together. Note that the first description was "assume as current" and the second description is hypothetical related to the first description.
(I used the asterisk as multiplication operator symbol).
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Re: Word Problem: Trouble transforming into mathematical equ

Postby jwroblewski44 on Wed Jun 05, 2013 2:00 pm

Thanks guys. You helped me a lot.
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