Question

The owner of a health food store is developing a new product that consists of peanuts and raisins. Raisins cost \$2.50$2.50dollar sign, 2, point, 50 per pound and peanuts cost \$3.50$3.50dollar sign, 3, point, 50 per pound. The owner wants to create 202020 pounds of the product that cost \$3.03$3.03dollar sign, 3, point, 03 per pound. Which of the following systems of equations can be used to determine the number of pounds of peanuts, ppp, and the number of pounds of raisins, rrr, that should be combined?

Answer 1

p + r = 20

`(3.50p+2.50r)/(20)` = 3.03

Explanation:

The total cost of the product when the peanuts and raisins are combined is:

3.50p + 2.50r

To obtain the per pound cost, this expression needs to be divided by the number of total pounds, 20.

`(3.50p+2.50r)/(20) =3.03`

**KA's explanation**

Answer 2

9.4 pound of raisin and 10.6 pound of peanut is required to make 20 pound of product

Explanation:

The cost of raisins is $2.5 per pound and the cost of peanut per pound is $3.50.

Let r represent the number of raisin pound and p represent the number of peanut pound. Since 20 pounds of a new product that consists of peanuts and raisins need to be produced, it can be represented by the equation:

p + r = 20 (1)

The new product would cost $3.03, therefore:

3.5p + 2.5r = 3.03(20)

3.5p + 2.5r = 60.6 (2)

We have to solve equation (1) and (2) simultaneously. First multiply (1) by 2.5 to get 2.5p + 2.5r = 50. Subtract 2.5p + 2.5r = 50 from equation (2):

p = 10.6 pound

Put p = 10.6 in equation (1)

10.6 + r = 20

r = 20 - 10.6 = 9.4

r = 9.4 pound

9.4 pound of raisin and 10.6 pound of peanut is required to make 20 pound of product