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 the mixture is $27.00. How much of each ingredient did the store use?

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 the mixture is $27.00. How much of each ingredient did the store use?

Answer 1

Gummy candy: 11 pounds x 2 = 22 pounds

Jelly beans: 11 pounds x 1 = 11 pounds
Hard candy: 11 pounds x 0 = 0 pounds

Answer 2

Absolutely useless by the robot tutor just to state answers, especially

if they are wrong.

amount of jelly beans --- x pounds
amount of gummy ---- 2x pounds
amount of hard candy --- y pounds

equation base on number of pounds:
x+2x+y = 11
y = -3x + 11

equation based on cost:
2(2x) + 3x + 3y = 27
7x + 3(-3x + 11) = 27
-2x = -6
x = 3

So we need 3 pounds of Jelly Beans, 6 pounds of Gummies
and 2 pounds of hard candy

Answer 3

Let's assume the store used x pounds of jelly beans.

According to the given information, the store used 2 times as many gummy candy pieces as jelly beans, so it used 2x pounds of gummy candy.

The total weight of jelly beans and gummy candy is x + 2x = 3x pounds.

The total weight of hard candy is 11 - 3x pounds.

The cost of jelly beans is $3 per pound, so the cost of x pounds of jelly beans is 3x dollars.

The cost of gummy candy is $2 per pound, so the cost of 2x pounds of gummy candy is 2 * 2x = 4x dollars.

The cost of hard candy is $3 per pound, so the cost of (11 - 3x) pounds of hard candy is 3 * (11 - 3x) = 33 - 9x dollars.

The total cost of the mixture is $27, so the equation is:

3x + 4x + 33 - 9x = 27.

Combining like terms, the equation becomes:

-2x + 33 = 27.

Subtracting 33 from both sides of the equation gives:

-2x = -6.

Dividing both sides by -2 gives:

x = 3.

Therefore, the store used 3 pounds of jelly beans, and it used 2 * 3 = 6 pounds of gummy candy.

The weight of hard candy is 11 - 3 = 8 pounds.

So, the store used 3 pounds of jelly beans, 6 pounds of gummy candy, and 8 pounds of hard candy.

Answer 4

To solve this problem, we can break it down into a system of equations.

Let's assume that the store used x pounds of jelly beans. Since the mixture calls for two times as many gummy candy pieces as jelly beans, it used 2x pounds of gummy candy.

The total weight of the mixture is 11 pounds. So, we can write the equation: x + 2x + y = 11, where y represents the weight of the hard candy.

The cost of gummy candy is $2.00 per pound, so the cost of the gummy candy used is 2x * $2.00 = $4x
The cost of jelly beans is $3.00 per pound, so the cost of the jelly beans used is x * $3.00 = $3x
The cost of hard candy is $3.00 per pound, so the cost of the hard candy used is y * $3.00 = $3y

The total cost of the mixture is $27.00. So, we can write the equation: 4x + 3x + 3y = 27

Now we have a system of equations:
x + 2x + y = 11
4x + 3x + 3y = 27

To solve this system of equations, we can use the method of substitution or elimination.

Let's use the method of substitution:
From the first equation, we can express y in terms of x:
y = 11 - 3x

Substituting this value of y in the second equation:
4x + 3x + 3(11 - 3x) = 27
7x + 33 - 9x = 27
-2x = -6
x = 3

Now we can substitute the value of x back into the equation y = 11 - 3x:
y = 11 - 3(3)
y = 11 - 9
y = 2

So, the store used 3 pounds of jelly beans, 2 * 3 = 6 pounds of gummy candy, and 2 pounds of hard candy.