Question

Hello there I need help with this question please make it simple I am in year 9

Answer 1

Use the substitution method to solve the system of equations.

Let k be the cost of a knife and s be the cost of a spoon.

Since a knife is four times the cost of a spoon, then:

`k=4s`

Since 12 spoons and 16 knives cost 105.64, then:

`12s+16k=105.64`

Replace the expression for k in terms of s into the second equation:

`12s+16(4s)=105.64`

We obtained an equation in a single variable. Solve for s:

`\begin{gathered} \Rightarrow12s+64s=105.64 \\ \Rightarrow76s=105.64 \\ \Rightarrow s=(105.64)/(76) \\ \therefore s=1.39 \end{gathered}`

Replace the value of s into the expression for k to find the cost of a knife:

`\begin{gathered} k=4s \\ \Rightarrow k=4(1.39) \\ \therefore k=5.56 \end{gathered}`

Therefore, the cost of one knife is equal to £5.56.