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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).

Respuesta :

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,

[tex]M(n+p)=Nn+Pp[/tex]

Now, put the values in the above equation.

[tex]\begin{gathered} 5.91\times(13+p)=3.1\times13+7.5\times p \\ 5.91\times13+5.91p=3.1\times13+7.5\times p \\ 5.91p-7.5\times p=3.1\times13-5.91\times13 \\ -1.59p=13(3.1-5.91) \\ -1.59p=13\times(-2.81) \\ -1.59p=-36.53 \\ p=\frac{-36.53}{-1.59} \\ p\cong23\text{ pounds} \end{gathered}[/tex]

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

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