Question

A grocer wants to mix two kinds of candy. One kind sells for $1.80 per pound, and the other sells for $3.00 per pound. He wants to mix a total of 15 pounds and sell it for $1.95 per pound. How many pounds of each kind should he use in the new mix? (Round off the answers to the nearest hundredth.)

Answer 1

the grocer should mix approximately 13.12 pounds of 1st candy.

the grocer should mix approximately 1.88 pounds of 2nd candy.

Explanation:

From the given information.

let x represent the pounds of the first candy and y represent the pound of the second candy

We are being told that the grocer wants to sell a total of 15 pounds,

so;

`x+y = 15 \\ \\x= 15-y` ----- (1)

also; we are being informed that one kind sells for $1.80 per pound, and the other sells for $3.00 per pound. and he wants to mix a total of 15 pounds and sell it for $1.95 per pound.

So;

`1.80 x + 3y = 15(1.95)`

`1.80x + 3y = 29.25` ------(2)

Replacing equation (1) into 2 ; we have :

1.8(15 - y) + 3y = 29.25

27 - 1.8y + 3y = 29.25

- 1.8y + 3y = 29.25 - 27

1.2y = 2.25

y = 2.25/1.2

y = 1.88

Therefore, the grocer should mix approximately 1.88 pounds of 2nd candy.

Replacing the value of y into equation (1)

x = 15 - y

x= 15 - 1.88

x = 13.12

Therefore, the grocer should mix approximately 13.12 pounds of 1st candy.

Answer 2

Answer: 13.12 pounds of the candy that sells for $1.80 per pound 1.88 pounds of the candy that sells for $3 per pound should be in the mixture.

Explanation:

Let x represent the number of pounds of the candy that sells for $1.80 per pound that should be in the mixture.

Let y represent the number of pounds of the candy that sells for $3.00 per pound that should be in the mixture.

The total pounds of both candies in the mixture is 15. It means that

x + y = 15

Since he wants to sell the mixture for $1.95 per pound, the cost of the mixture per pound would be 1.95(x + y)

The equation would be

1.8x + 3y = 1.95(x + y)- - - - - - - - - - 1

Substituting x = 15 - y into equation 1, it becomes

1.8(15 - y) + 3y = 1.95(15 - y + y)

27 - 1.8y + 3y = 29.25

- 1.8y + 3y = 29.25 + 27

1.2y = 2.25

y = 2.25/1.2

y = 1.88

x = 15 - y = 15 - 1.88

x = 15 - 1.88 = 13.12