one fork and five knives balance 4 spoons.also 3 knives balance 2 forks and 2 spoons.then how many forks balance 2 knives and 2 spoons

Question

question is been relates to junior maths olympiad prectice test.for class 5

Answer 1

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.