How many pounds of candy A are in the mixture? How many pounds of candy B are in the mixture?

Question

Candy A costs $2.50 per pound

 

Candy B costs $4.50 per pound

 

Ten pounds of the combined mixture cost $37.00

Answer 1

Let A = pounds of Candy A

Let B = pounds of Candy B

 

 

2.50A + 4.50B = 37.00

 

A + B = 10

 

Therefore,

A = 10 - B

 

Let's substitute (10 - B) wherever we see A in the first equation.

 

So

2.50(10 - B) + 4.50B = 37

 

Distribute the 2.50 through

 

25 - 2.50B + 4.50B = 37

 

Combine the like terms

 

25 + 2B = 37

 

2B = 12

 

B = 6

 

Substitute this in our original equation

 

A + B = 10

 

A + 6 = 10

 

A = 4

 

Therefore we have 4 pounds of Candy A and 6 pounds of Candy B in the mixture.