Word Problem

Question

A candy store wants to create a mix using two hard candies. One is priced at $5.45 per pound, and the other is $7.33 per pound. How many pounds of the $7.33 candy should be mixed with 11 pounds of the $5.45 candy to sell the mixture for $6.14 per pound?

Answer 1

Students often find mixture problems difficult.

Whenever possible in a word problem, let the variable represent the thing you are trying to find, which is the number of pounds of the $7.33 candy to add. So, let x represent this number. Then, since we are mixing it with the other candy, the total amount of candy we will have is  11+x pounds, which will sell for $6.14 a pound.

 

So, here are the facts:

We are starting with 11 pounds of $5.45 candy. The total value of this candy is pounds times price per pound, or   11x5.45 = $59.95

 

We are adding x pounds of  $7.33 candy, with a price of  $7.33x

 

The total will be  (11+x) pounds of $6.14 candy, which will have a price of   $6.14(11+x).

 

Now, the sum of the two different candies has to be the same as this total, giving us the equation

 

          59.95 + 7.33x = 6.14(11+x)

 

So this is the equation for us to solve.

 

First, use the distributive property to remove the parentheses:

 

6.14(11+x) = 67.54 + 6.14x

 

We now have   59.95 + 7.33x = 67.54 + 6.14x

 

Now we need to get our x's to one side and the numbers to the other side. We will subtract  59.95 from both sides, and subtract 6.14x from both sides, giving us

 

                1.19x = 7.59

 

Now, to get x by itself, we divide both sides by 1.19, to get

 

                      x = 6.38 pounds of $7.33 candy.

 

The answer is rounded to the nearest hundredth.

Answer 2

We can assume that  we will mix X pounds of candies of $7.33

now we can write an equation:

7.33X+5.45x11=6.14(X+11)

7.33X+59.95=6.14X+67.54 subtract 6.14X from both sides of the equation

1.19X+59.95=67.54  subtract 59.95   from both sides of the equation

1.19X=7.59 divide both sides by 1.19

X equals about 6.378 pounds