Question

A candy store makes a 12-lb mixture of gummy bears, jelly beans, and Runts. The cost of gummy bears is $1.50 per pound, jelly beans cost $1.00 per pound, and Runts cost $1.00 per pound. The mixture calls for three times as many gummy bears as jelly beans. The total cost of the mixture is $15.00. How much of each ingredient did the store use?

Answer 1

g= 6

j = 2

r= 4

Explanation:

Gummy bears = $1.50 per pound

Jelly beans = $1.00 per pound

Runt = $1.00 per pound

Total cost of the mixture = $15.00

Let

g = quantity of gummy bears

j = quantity of jelly beans

r = quantity of runts

g + j + r=12 (1)

1.5g + 1.0j + 1.0r = 15 (2)

three times as many gummy bears as jelly beans.

g=3j

Substitute g=3j into 1

g + j + r = 12

3j + j + r =12

4j + r =12 (3)

Substitute g=3j into 2

1.5g + 1.0j + 1.0r = 15

1.5(3j) + 1.0j + 1.0r =15

4.5j + 1.0j + 1.0r = 15

5.5j + 1.0r =15 (4)

4j + r =12 (3)

5.5j + 1.0r =15 (4)

Subtract (3) from (4)

5.5j - 4j = 15-12

1.5j = 3

Divide both sides by 1.5

j = 3/1.5

= 2

j = 2

Substitute j = 2 into (3)

4j + r =12

4(2) + r =12

8 + r = 12

r= 12-8

r= 4

Substitute j=2 and r= 4 into (1)

g + j + r=12

g + 2 + 4 = 12

g + 6 = 12

g = 12-6

=6

g=6

g= 6

j = 2

r= 4