Question

A candy store makes a 11-lb mixture of gummy bears, jelly beans, and gobstoppers. The cost of gummy bears is $2.00 per pound, jelly beans cost $2.00 per pound, and gobstoppers cost $1.00 per pound. The mixture calls for three times as many gummy bears as jelly beans. The total cost of the mixture is $200.00. How much of each ingredient did the store use?

Answer 1

To determine how much of each candy type was used in an 11-lb mixture costing $200, a system of equations is set up and solved, yielding approximately 4.72 pounds of jelly beans, 14.16 pounds of gummy bears, and 2.12 pounds of gobstoppers.

Step-by-step explanation:

The question involves creating an equation to solve a word problem related to a mixture of different types of candy costing different prices. To figure out how much of each ingredient the store used, we need to set up a system of equations based on the given information.

• Let x be the weight of jelly beans in pounds.
• Let 3x be the weight of gummy bears in pounds, which is three times the weight of jelly beans.
• Let y be the weight of gobstoppers in pounds.

The mixture weighs 11 pounds in total, which gives us the equation:

x + 3x + y = 11

The total cost of the mixture is $200, which gives us another equation based on the cost per pound:

2x + 2(3x) + 1y = 200

We then solve for x and y using these equations. Simplifying the cost equation:

2x + 6x + y = 200

8x + y = 200

To find the weight of each type of candy:

1. From the weight equation, solve for y: y = 11 - 4x.
2. Substitute y in the cost equation: 8x + (11 - 4x) = 200.
3. Solve for x: 4x = 189, so x is approximately 4.72 pounds of jelly beans.
4. Calculate y: y = 11 - 4(4.72), so y is approximately 2.12 pounds of gobstoppers.
5. The weight of gummy bears is 3x, or approximately 14.16 pounds.

Therefore, the store used about 4.72 pounds of jelly beans, 14.16 pounds of gummy bears, and 2.12 pounds of gobstoppers to make the 11-lb candy mixture costing $200.