Mathematics
OpenStudy (anonymous):

Yet another word problem.... The cooks are counting spoons, knives and forks. There were 10 more forks than knives and 10 more spoons than forks. All together there are 363 utensils. How many forks?

OpenStudy (anonymous):

Okay, what have you tried?

OpenStudy (turingtest):

let x=#spoons y=#forks z=#knives now translate each of the three statements about the numbers of utensils given above into "math language" starting with "There were 10 more forks than knives" how would you write that using the x, y, and z ?

OpenStudy (anonymous):

I think OP will sit silent until someone post the answer.

OpenStudy (turingtest):

That is their problem... -For my two cents, whoever just posts an answer without sufficient explanation is abusing this site and does not deserve any medal or recognition. ^let that encourage the next 'sniper' (as the recent announcement has coined) to post the answer.

OpenStudy (anonymous):

I'm sorry. I was in another tab. This is what I've tried: X= number of forks x-10= number of knives x+10= number of spoons So, I wrote it out like this: 1(x+10) + 1 (x-10)= 363.

OpenStudy (turingtest):

you are missing a term (x+10) + (x-10) = 363 ^#spoons ^#knives ^#utensils where is the number of forks?

OpenStudy (anonymous):

Sadly, I have no clue where to put the number of forks in this equation. If I did, I wouldn't be on this site.

OpenStudy (anonymous):

S = #spoons F = #forks K = #knives 10 + K = F 10 + F = S

OpenStudy (turingtest):

that was how I was going to do it

OpenStudy (anonymous):

Now add them together, K+10+K+20+k = 363 K = 111 F = 121

OpenStudy (anonymous):

assuming my algebra is correct.

OpenStudy (anonymous):

Saying something @TuringTest ? :P

OpenStudy (turingtest):

There were 10 more forks than knives K=F+10 10 more spoons than forks S+10=F I believe you have misinterpreted the statements, though it still gives the correct number of forks... I feel like I'm getting a little confused, I'm pretty tired, but...

OpenStudy (turingtest):

F+K+S=F+(F+10)+(F-10) which is what I implied above

OpenStudy (turingtest):

...so I was saying you switched knives and spoons is all

OpenStudy (anonymous):

I am tired too :( But "10 more forks than knives" doesn't that mean F=10+K?

OpenStudy (anonymous):

I don't understand how " 10 more spoons than forks" could imply that more forks than spoon?

OpenStudy (turingtest):

I keep doubting myself, I give up

OpenStudy (anonymous):

Please, more eyes! None of these responses are helping me. If we don't know the value of F, how do you work out (F+10)???

OpenStudy (turingtest):

we do at least agree on the value of F blue

OpenStudy (anonymous):

The value of F is an unknown. It's the number of forks. How do you subtract from it? Gah- this is where I get stuck in algebra.

OpenStudy (anonymous):

My final answer should be right :)

OpenStudy (turingtest):

finally I'm wrong

OpenStudy (turingtest):

I see it now

OpenStudy (anonymous):

Okay this is my final answer: "10 more forks than knives" means to there are more forks than knives, and the statement implies \[F-K=10 \implies F=10+K \]

OpenStudy (turingtest):

yeah, I just had a complete lapse in brain function 1,000 medals to FFM!

OpenStudy (phi):

This is straight forward, except possibly for interpreting the English. "10 more forks than knives" may be confusing. But if I said, I have 10 more dollars than you, it's intuitive that I have more dollars than you: M= Y+10 (if we give you 10 dollars you will have as much as me.) With that said, we can copy FFM's from above S = #spoons F = #forks K = #knives 10 + K = F or K= F-10 "10 more forks than knives" 10 + F = S or F= S-10 "10 more spoons than forks" K+F+S= 363 F-10+F+F+10 = 363 3F=363 F= 121 which is what has already been posted.

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