Even though there are two different types of mixes, the process for solving them is the same.
Suppose the owner of a candy store mixes two types of candies. She decides to create a 20pound
mixture of raspberryflavored gumdrops and cherryflavored jelly beans. The gumdrops sell for $0.95 per pound and the jelly beans sell for $1.20 per pound. She plans to sell the mix for $1.10 per pound. How many pounds of each candy should she use in her mix?
First, since two quantities are to be mixed together to produce one mixture, we need to recognize that we will set up an
equation that shows the following:
total cost of gumdrops plus
total cost of jelly beans equals the
total cost of mixture
To arrive at the equation, it is typically helpful to use a
table illustrating the problem such as the following:
Type of Candy

Cost of Candy (unit price)

Amount of Candy (in pounds)

Total Cost (in dollars)

gumdrops




jelly beans








The first column shows the types of candy involved, cost is displayed in the second column, amount of each type of candy is listed in the third column, and the fourth column is the
product of each cost and each amount for each type of candy. The total cost of the
mixture is found by multiplying the cost of each type candy times the amount of each type of candy used in the mixture. The total cost column will be used to write the equation.
The candy store owner knows that she wants the total amount of the
mixture of candy to be 20 pounds. However, she does not know how many pounds of each type to mix. That is the objective of the problem. So in the “Amount of Candy” column we will use
x to represent the amount of gumdrops. Then the “total pounds of candy minus
x” will represent the amount of jelly beans: (20 – x). The last column demonstrates that the price of each type candy multiplied times the amount of each type candy represents the total cost of each type candy. The last column is what we use to write the equation.
Remember:
total cost of gumdrops plus
total cost of jelly beans equals the
total cost of mixture
So, using the information in the last column:
We are ready to solve the
equation to find the amount of each type of candy the store owner should use in her mixture.

First distribute to remove parentheses 

Now multiply the equation by 100 

Solve for x 


pounds 

Since x represents the amount of gumdrops to be used in the
mixture the candy store owner will use 8 pounds of gumdrops. From column three of the table, you can see that the amount of jelly beans to be used is (20  x). Substituting 8 for the
x, we see that the store owner needs to use (20  8) which is 12 pounds of jelly beans to create the desired mix.
We have now learned the candy store owner will mix 8 pounds of raspberryflavored gumdrops that cost $0.95 per pound and 12 pounds of cherryflavored jelly beans that cost $1.20 per pound to create a
mixture of 20 pounds of candy that sells for $1.10 per pound.