A candy store makes a 9-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, hard candy cost $3.00 per pound. The mixture calls for two times as many gummy candy piece as jelly beans. The total cost of the mixture is $23.00. How much of each ingredient did the store use?

Question

hero · Answer

g = pounds of gummy
 j = pounds of jelly
h = pounds of hard

     g + j + h = 9
2g + 3j + 3h = 23
                 g = 2j

hero · Answer

g + j + h = 9 represents the total pounds of all the candy.

2g + 3j + 3h = 23 represents the total cost of all the candy

g = 2j represents that the amount of gummy is twice the amount of jelly.

hero · Answer

Since g = 2j we can substitute 2j in place of g in the first two equations to get:

       2j + j + h = 9
2(2j) + 3j + 3j = 23

Combining the j terms together:

  $3\color\red{\text{j}}   + \color\green{\text{h}} = 9$
$7\color\red{\text{j}} + 3\color\green{\text{h}} = 23$

Now we have a system of two equations


@DestinyMcGee2015  Can you solve the system of two equations?

anonymous · Answer

Yes, thank you so much !

hero · Answer

Okay, solve it real quick and let me know what you get.