Question

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?

Answer 1

Okay, what have you tried?

Answer 2

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 ?

Answer 3

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

Answer 4

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.

Answer 5

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.

Answer 6

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

Answer 7

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.

Answer 8

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

10 + K = F
10 + F = S

Answer 9

that was how I was going to do it

Answer 10

Now add them together,

K+10+K+20+k = 363

K = 111

F = 121

Answer 11

assuming my algebra is correct.

Answer 12

Saying something @TuringTest ? :P

Answer 13

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...

Answer 14

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

Answer 15

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

Answer 16

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

Answer 17

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

Answer 18

I keep doubting myself, I give up

Answer 19

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)???

Answer 20

we do at least agree on the value of F blue

Answer 21

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.

Answer 22

My final answer should be right :)

Answer 23

finally I'm wrong

Answer 24

I see it now

Answer 25

Okay this is my final answer:

"10 more forks than knives" means to there are more forks than knives, and the statement implies

\[F-K=10 \implies F=10+K \]

Answer 26

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

Answer 27

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.