Question

A candy store makes a 13–pound mixture of gummy bears, jelly beans, and gobstoppers. The cost of gummy bears is $1.00 per pound, jelly beans cost $2.00 per pound, and gobstoppers cost $2.00 per pound. The mixture calls for three times as many gummy bears as jelly beans. The total cost of the mixture is $20.00. How much of each ingredient did the store use?
8 lbs gummy bears, 2 lbs jelly beans, 3 lbs gobstoppers
3 lbs gummy bears, 6 lbs jelly beans, 4 lbs gobstoppers
6 lbs gummy bears, 2 lbs jelly beans, 5 lbs gobstoppers
8 lbs gummy bears, 3 lbs jelly beans, 2 lbs gobstoppers

Answer 1

Let the amount of gummy bears used be x, that of jelly beans y and gobstoppers z, then
x + y + z = 13 . . . (1)
x + 2y + 2z = 20 . . . (2)
x = 3y . . . (3)

Putting (3) into (1) and (2) gives
4y + z = 13 . . . (4)
5y + 2z = 20 . . . (5)

(4) * 2 => 8y + 2z = 26 . . . (6)

(6) - (5) => 3y = 6
y = 2

From (3): x = 3(2) = 6
From (4): 4(2) + z = 13
z = 13 - 8 = 5

Therefore, there were 6 lbs gummy bears, 2 lbs jelly beans, 5 lbs gobstoppers in the mixture.

Answer 2

X = gummy bears, y = jelly beans, z = gobstoppers
x + y + z = 13
x + 2y + 2z = 20
x = 3y

3y + y + z = 13
4y + z = 13

3y + 2y + 2z = 20
5y + 2z = 20

4y + z = 13....multiply by -2
5y + 2z = 20
-----------------
-8y - 2z = -26
5y + 2z = 20
---------------add
-3y = -6
y = 2........2 lbs jelly beans

x = 3y
x = 3(2)
x = 6....6 lbs gummy bears

x + y + z = 13
6 + 2 + z = 13
8 + z = 13
z = 13 - 8
z = 5........5 lbs gobstoppers

so we have : 6 lbs gummy bears (x), 2 lbs jelly beans (y), and 5 lbs gobstoppers (z)