Question

Can someone please help answer the attached?

Answer 1

The variables we need to use in the question are defined. We will call the price of a knife as
`k` and the price of a spoon as
`s`.

The total price of
`12` spoons and
`16` knives is then given. Let's write knives instead of
`4` spoons.

• 
  `12s+16k=105.64`
• 
  `3k+16k=105.64`
• 
  `k=5.56` per knife.

Answer 2

Answer: 5.56 pounds

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Step-by-step explanation:

k = cost of one knife

s = cost of one spoon

costs are in pounds

12s = cost of 12 spoons

16k = cost of 16 knives

12s+16k = 105.64 pounds is the total cost

We can replace k with 4s because of the phrasing "a knife is 4 times the cost of a spoon". Whatever s might be, quadruple it and it leads us to the value of k.

So,

12s+16k = 105.64

12s+16(4s) = 105.64

12s+64s = 105.64

76s = 105.64

s = 105.64/76

s = 1.39 pounds is the cost of one spoon

k = 4s = 4*1.39 = 5.56 pounds is the cost of one knife

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Check:

1 spoon = 1.39 pounds

12 spoons = 12*1.39 = 16.68 pounds

1 knife = 5.56 pounds

16 knives = 16*5.56 = 88.96 pounds

12 spoons + 16 knives = 16.68+88.96 = 105.64 pounds total

This fully verifies the answer.