How many pounds of each candy should the owner of a candy store use in her mix?!

Question: How many pounds of each candy should the owner of a candy store use in her mix?
Suppose the owner of a candy store mixes two types of candies. She decides to create a 30-pound mixture of raspberry-flavored gumdrops and cherry-flavored jelly beans. The gumdrops sell for $0.90 per pound and the jelly beans sell for $1.25 per pound. She plans to sell the mix for $1 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 equal 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 Amount of Candy Total Cost
(unit price) (in pounds) (in dollars)

Gumdrops 0.90 x 0.90(x)
Jelly beans 1.25 (30 - x) 1.25(30 - x)
Mixture 1.0 30 1.00(30)

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 30 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: (30 – 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.


Ttal cost of gumdrops plus total cost of jelly beans equals the total cost of mixture

So, using the information in the last column:

0.90x + 1.25(30 - x) = 1.00(30)

We are ready to solve the equation to find the amount of each type of candy the store owner should use in her mixture.

0.90x + 1.25(30 - x) = 1.00(30)................First distribute to remove parentheses

0.90x + 37.5 - 1.25x = 30.00...................Now multiply the equation by 100
90x + 3750 - 125x = 3000.......................Solve for x
-35x = -750
x = 21.43 pounds

Since x represents the amount of gumdrops to be used in the mixture the candy store owner will use 21 pounds of gumdrops. From column three of the table, you can see that the amount of jelly beans to be used is (30 - x). Substituting 21 for the x, we see that the store owner needs to use (30 - 21) which is 9 pounds of jelly beans to create the desired mix.

We have now learned the candy store owner will mix 21 pounds of raspberry-flavored gumdrops that cost $0.90 per pound and 9 pounds of cherry-flavored jelly beans that cost $1.25 per pound to create a mixture of 30 pounds of candy that sells for $1.00 per pound.

Depends on how much profit she wants to make...

--- so the answer is d) Not enough information

--- even then the question still doesn't have enough info because it doesn't say what ratio she wants in the mix...She could just use 29 pounds gumdrops and 1 pound jelly beans or she could use 27 pounds gumdrops and 3 pounds jelly wonder American kids are so stupid if this is the questions they are being asked...

--- go tell your teacher they are an idiot for me would ya ? Thanks !!!



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