Question

A store has two types of nuts that they will mix together to make a mixture worth $5.91 per pound. If thestore uses 13 pounds of a nut that costs $3.10 per pound, how many of pounds of nuts that cost $7.50 perpound should be added to make the mixture?The store should addpounds of nuts worth $7.50 per pound (round to the nearest wholepound - NO COMMAS).

Answer 1

Given:

The cost of mixture per pound, M= $5.91.

The quantity of nuts taken first , n=13 pounds.

The cost of nuts per pound, which was taken first, N=$3.10.

The cost of nuts per pound taken second, P=$7.50.

Let p be the quantity of nuts taken second.

Hence, we can write,

`M(n+p)=Nn+Pp`

Now, put the values in the above equation.

`\begin{gathered} 5.91*(13+p)=3.1*13+7.5* p \\ 5.91*13+5.91p=3.1*13+7.5* p \\ 5.91p-7.5* p=3.1*13-5.91*13 \\ -1.59p=13(3.1-5.91) \\ -1.59p=13*(-2.81) \\ -1.59p=-36.53 \\ p=(-36.53)/(-1.59) \\ p\cong23\text{ pounds} \end{gathered}`

Therefore, 23 pounds of nuts that cost $7.50 per pound is added to make the mixture.