Question

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, 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 the mixture is $23.00. How much of each ingredient did the store use?

Answer 1

Let

x--------> the amount of gummy candy in pounds

y--------> the amount of jelly beans in pounds

z--------> the amount of hard candy in pounds

we know that

`x+y+z=9` --------> equation
`1`

`2x+3y+3z=23` --------> equation
`2`

`x=2y` --------> equation
`3`

Substitute equation
`3` in equation
`1` and equation
`2`

`[2y]+y+z=9` ----->
`3y+z=9` ------> equation
`4`

`2[2y]+3y+3z=23` ----->
`7y+3z=23` ------> equation
`5`

using a graphing tool ------> Solve the system of equations

see the attached figure

the solution is the point
`(3,2)`

`z=3\ pounds\\y=2\ pounds`

Find the value of x

`x=2y`

`x=2*2=4\ pounds`

therefore

the answer is

the amount of gummy candy is
`4\ pounds`

the amount of jelly beans is
`2\ pounds`

the amount of hard candy is
`3\ pounds`