Question

A food store makes a 10-pound mixture of peanuts, cashews, and raisins. The mixture has twice as many peanuts as cashews. Peanuts cost $1 per pound, cashews cost $2 per pound, and raisins cost $2 per pound. The total cost of the mixture is $16. How much of each ingredient did the store use to make the mixture?
I know the equations are likely

X = Peanuts

Y = Cashews

Z = Raisins


X + 2Y + 2Z = 16

2Y = X

X + Y + Z = 10

Answer 1

Answer:

The number of pounds peanuts = x = 4 pounds

The number of pounds cashews = y = 2 pounds

The number of pounds raisins be equal to z = 4 pounds

Step-by-step explanation:

The number pounds of the mixture = 10

Let the number of pounds peanuts = x

Let the number of pounds cashews = y

Let the number of pounds raisins be equal to z

Hence,

x + y + z = 10

The mixture has twice as many peanuts as cashews.

2y= x

= 2y + y + z = 10

= 3y + z = 10

z = 10 - 3y

Peanuts cost $1 per pound, cashews cost $2 per pound, and raisins cost $2 per pound. The total cost of the mixture is $16.

x × $1 + y × $2 × z × $2 = $16

x + 2y + 2z = 16......Equation 2

We Substitute.(2y = x), (z = 10 - 3y)

2y + 2y + 2(10 - 3y) = 16

4y + 20 - 6y = 16

20 - 16 = 6y - 4y

4 = 2y

y = 4/2

y = 2 pounds

z = 10 - 3y

z = 10 - 3(2)

z = 10 - 6

z = 4 pounds

2y= x

2(2) = x

x = 4 pounds

How much of each ingredient did the store use to make the mixture?

The number of pounds peanuts = x = 4 pounds

The number of pounds cashews = y = 2 pounds

The number of pounds raisins be equal to z = 4 pounds