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 $3\ pounds$

Answer 2

Let the amount of gummy candy used be x, that of jelly beans be y and that of hard copy be z, then
x + y + z = 9 . . . (1)
2x = y . . . (2)
2x + 3y + 3z = 23 . . . (3)

Putting (2) into (1) and (3) gives
x + 2x + z = 9
3x + z = 9 . . . (4)
2x + 3(2x) + 3z = 23
8x + 3z = 23 . . . (5)

(4) x 3 => 9x + 3z = 27 . . . (6)
(5) - (6) => -x = -4
x = 4

From (2), 2(4) = y
y = 8

From (1), 4 + 8 + z = 9
z = 9 - 12 = -3