my question will be in the description because it is too long.

Question

A grocer wants to mix two kinds of candy. One kind sells for $1.25per pound, and the other sells for $2.65 per pound. He wants to mix a total of 15 pounds and sell it for $1.90 per pound. How many pounds of each kind should he use in the new mix? (Round off the answers to the nearest hundredth)                                                                      NUMBER POUNDS OF CANDY THAT COSTS $1.25?

NUMBER OF POUNDS OF CANDY THAT COSTS $2.65?

Answer 1

You can write two equations from the information given, then you can solve the system for both quantities.

A = weight of $1.25 candy.

B = weight of $2.65 candy.

 

The total weight of the mixture will be 15 pounds.

A + B = 15

B = 15-A

 

The value of A in the mixture is 1.25A

The value of B in the mixture is 2.65B

The total cost of the ingredients is 1.25A + 2.65B

The cost per pound of the mixture is (1.25A + 2.65B) / 15

(1.25A + 2.65B) / 15 = 1.90

 

We have an equation with two variables, but we can solve that first equation above for B in terms of A, then substitute that for B in the second one.

 

(1.25A + 2.65B) / 15 = 1.90

1.25A + 2.65B = (15)(1.9) = 28.5     clear the denominator

 

Substitute (15-A) for B

1.25A + 2.65(15-A) = 28.5

1.25A + 39.75 - 2.65A  = 28.5

1.25A - 2.65A = 28.5 - 39.75

-1.4A = -11.25

A = 8.04

B = 15 - 8.04 = 6.96

 

Check:

(1.25A + 2.65B) / 15 =? 1.90

[(1.25)(8.04) + (2.65)(6.96)] / 15 = (10.05 + 18.44) / 15 = 28.49 / 15 = 1.90  It checks!