Dalia C. answered • 01/19/17

Tutor

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Highly Qualified Mathematics and Physics for grades 7-12 in CT.

let f = forks

let s = spoons

let k = knives

then,

f + 5k = 4s, one fork and 5 knives balance 4 spoons.

and,

3k = 2f + 2s, 3 knives balance 2 forks and 2 spoons.

isolate the term for the spoons in both equations to get

4s = 5k + f

2s = 3k - 2f, multiply this equation by -2 to solve the system using elimination to get

-4s = -6k + 4f

0 = -k + 5f, or

**k = 5f,**

**2k = 10f**

substitute k value into one of the original equations;

3k = 2f + 2s

3(5f) = 2f + 2s

15f = 2f + 2s

**13f = 2s, or 2s = 13f**

therefore

**2s + 2k = 13f + 10f = 23f ... this means it takes 23 forks to balance two spoons and 2 knives.**