Question

A candy store makes an 11- pound mixture of gummy candy, jelly beans, and hard candy. The cost of gummy candy is $2.00 per pound, jelly beans cost $3.00 per pound, and hard candy costs $3.00 per pound. The mixture calls for two times as many gummy candy pieces as jelly beans. The total cost of this mixture is $27.00. How much of each ingredient did the store use?

1. 6 lbs. gummy, 3 lbs. jelly beans, 2 lbs hard candy
2. 3 lbs. gummy candy, 2 lbs. jelly beans, 6 lbs hard candy
3. 6 lbs gummy, 2 lbs jelly beans, 3 lbs. hard candy
4. 2 lbs gummy candy, 3 lbs. jelly beans, 6 lbs hard candy

Answer 1

The answer is given away by the problem... "the mixture calls for two times as many gummy candy pieced as jelly beans." the only answer with 2x the amount of gummies as jelly beans is

6lb gummy, 3lb jelly, 2lb hard

Answer 2

From the problem above, we have three unknowns, we let

x = gummy
y = jelly beans
z = hard candy

We need to set up three equations from the problem above to be able to solve it. We do as follows:

x + y + z = 11
2x + 3y + 3z = 27
x = 2y

Solving simultaneously,

y = 3
z = 2
x = 6

Therefore, the correct answer from the choices listed above is option 1, 6 lbs. gummy, 3 lbs. jelly beans, 2 lbs hard candy.