Question

Colin is making a 10-lb bag of trail mix for his upcoming backpacking trip. If chocolates cost $2.00 per pound and mixed nuts cost $8.00 per pound and Colin has budget of $6.20 per pound of trail mix, how many pounds of each should he use? A) pounds of chocolate? B) Pounds of nuts?

Answer 1

• A) 3 pounds of chocolate.

,

• B) 7 Pounds of nuts.

Explanation:

• Let the number of pounds of chocolate he should use = c

,

• Let the number of pounds of nuts he should use = n

Colin is making a total of 10-lb bag of trail mix, therefore:

`\begin{gathered} c+n=10 \\ \implies c=10-n \end{gathered}`

• Chocolates cost $2.00 per pound and mixed nuts cost $8.00.

,

• Colin has a budget of $6.20 per pound of trail mix

,

• He needs to make 10 pounds of trail-mix.

`2.00c+8n=6.20*10\text{ pounds}`

We solve the two equations simultaneously.

Recall that c=10-n.

`c=10-7=3`

Therefore, Colin should use (A) 3 pounds of chocolate; and (B) 7 Pounds of nuts.