Question

Solve the following problem. It may be helpful to use draw a chart on scrap paper to organize the information and write the equation. Be sure to show all steps (V.E.S.T.) and work in order to receive full credit. A grocer wants to make a 10-pound mixture of cashews and peanuts that he can sell for $3.29 per pound. If cashews cost $5.60 per pound and peanuts cost $2.30 per pound, how many pounds of each must he mix?

Answer 1

The grocer will buy 7 pounds of peanuts and 3 pounds of cashews.

Explanation:

Since the grocer wants 10 pounds of peanut and cashew mixture, that means that the number of pounds of each added together will equal 10.

Let c equal the number of pounds of cashews, and p equal the number of pounds of peanuts.

c + p = 10

Since he wants to make the mix cost $3.29 per pound then that means the total cost to buy the supplies for the mix totals up to $3.29 times 10. The number of pounds of peanuts is their cost times p and the same goes for the cashews but times c, once added together should equal $3.29 times 10.

$5.60c + $2.30p = $3.29*10

Now since the cashews cost more per pound, there will be less of them in the mix, which also means that the ratio of peanuts to cashews will not be equal. So lets try this

$5.60 x 2 + $2.30 x 8 = $3.29 x 10

$11.20 + $18.40 = $32.90

​​​​​​​That does not work because $11.20 added to $18.40 does not equal $32.90 it actually ends up equaling $29.60, which means that there aren't enough cashews. So lets try taking away one pound of peanuts and adding one pound of cashews.

$5.60 x 3 + $2.30 x 7 = $3.29 x 10

$16.80 + $16.10 = $32.90

This is correct because $16.80 added to $16.10 does equal $32.90. Therefore meaning that the grocer will have to buy 7 pounds of peanuts and 3 pounds of cashews.

Answer 2

we can translate the problem into two equations. The first statement is translated to x + y = 10 where x represents the amount of cashews in the mix while y represents the amount of peanuts in the mixture. In this case, the second equation is translated to 5.60x + 2.30 y = 3.29*10. solving the two equations simultaneously, x is equal to 3 pounds while y is equal to 7 pounds

Step-by-step explanation