word problem

Question

a dealer has some hard candy worth $2.00 a pound and some worth $3.00 a pound. he wishes to make a mixture of 80 pounds that he can sell for $2.20 a pound. how many pounds of each kind should he use?

Answer 1

Let x = number of pounds of $2/lb candy

     80 - x = number of pounds of $3/lb candy

 

Then 2x + 3(80 - x) = 2.20(80)

 

          2x + 240 - 3x = 176

 

                             -x = -64

 

                              x = 64

 

Use 64 pounds of $2/lb candy and 16 pounds of $3/lb candy to make 80 pounds of candy that sells for  $2.20/lb.  

Answer 2

Let x represent the amount of cheaper candy and y the more expensive.

 

The value of the cheaper candy is 2x and the value of the more expensive is 3y. The total value is (80*2.2) or 176.

 

x + y = 80 thus y = 80-x

2x + 3y = 176

2x + 3(80-x) = 176

240 + 2x - 3x = 176

240 - x = 176

240 - 176 = x

64 = x

y = 80 - x = 16