How many pounds of candy selling for $1.75 a pound should be added to three pounds of candy selling for $4.50 a pound to create a blend, which will sell for $3.40 a pound?

Question

mathmate · Answer

Mixing/blending problems.
To solve these problems, set up an equation relating the total price of all the candies, and divide by the total weight.  Represent the  unknown by a variable (such as x) and solve for x.

"How many pounds of candy selling for $1.75 a pound"
So call this "how many" x (in pounds), so
Total cost of cheaper candy = 1.75x
total cost of expensive candy = 4.50(3)

Total cost = 1.75x+3(4.50)
Total weight = 3+x

Unit price of mixture = total cost / total weight
= (1.75x+3(4.50)) / (3+x) = 3.40
So solve for x
Cross multiply:
(1.75x+13.50)=3.40$\times$(3+x)
I will leave it to you to solve for x, which is the weight of candy costing $1.75 a pound.

Note: as a rough check, the unit price of the mixture must be between unit prices of the two components.  If not, there is probably a mistake.

anonymous · Answer

@mathmate what did you end up getting for x?

mathmate · Answer

Post your answer and I'll be glad to check it for you.  Please also include how you solved it.