Question

Need help with a math word problem for homework. Thank you in advance

Answer 1

Given:

A client is making a 10-lb bag of trail mix

The chocolates cost $4 per pound and mixed nuts cost $7 per pound

the client has a budget of $6.1 per pound

We will use the variables c and n to represent the number of pounds for chocolates and nuts

So, we have the following system of equations:

`\begin{gathered} c+n=10\rightarrow(1) \\ 4c+7n=6.1\cdot10\rightarrow(2) \end{gathered}`

Solving the system by substitution method

From equation (1)

`c=10-n\rightarrow(3)`

substitute with (c) from equation (3) into equation (2)

`\begin{gathered} 4(10-n)+7n=6.1\cdot10 \\ \end{gathered}`

solve the equation to find (n)

`\begin{gathered} 4\cdot10-4n+7n=6.1\cdot10 \\ -4n+7n=6.1\cdot10-4\cdot10 \\ 3n=21 \\ n=(21)/(3)=7 \end{gathered}`

Substitute with (n) into equation (3) to find (c)

`c=10-7=3`

so, the answer will be:

The number of pounds of chocolates = c = 3 pounds

The number of pounds of nuts = n = 7 pounds