Question

A food store makes a 11-lb mixture of oatmeal, crispies, and chocolate chips. The cost of oatmeal is $1.50 per pound, crispies cost $2.00 per pound, and chocolate chips cost $1.00 per pound. The mixture calls for twice as much oatmeal as crispies. The total cost of the mixture is $17.00. How much of each ingredient did the store use?

Answer 1

6 pounds of oatmeal, 3 pounds of crispies and 2 pounds of chocolate chips were used.

Explanation:

Let,

x be the pounds of oatmeal used

y be the pounds of crispies used

z be the pounds of chocolate

According to given statement;

1.50x+2.00y+1.00z = 17.00 Eqn 1

x+y+z = 11 Eqn 2

x = 2y Eqn 3

Putting x=2y in Eqn 2

2y+y+z = 11

3y+z = 11 Eqn 4

From Eqn 4

z = 11 - 3y Eqn 5

Putting value of x and z from Eqn 3 and Eqn 5 in Eqn 1

1.50(2y) + 2.00y + 1(11-3y) = 17.00

3y+2y+11-3y=17

`2y=17-11\\2y=6\\(2y)/(2)=(6)/(2)\\y=3`

Putting y = 3 in Eqn 3

x= 2(3)

x= 6

Putting in Eqn 2

6 + 3 + z = 11

z = 11-9

z= 2

Hence,

6 pounds of oatmeal, 3 pounds of crispies and 2 pounds of chocolate chips were used.