Question

A grocer wants to mix two kinds of candy. One kind sells for $1.10 $ ⁢ 1.10 per pound, and the other sells for $2.55 $ ⁢ 2.55 per pound. He wants to mix a total of 28 28 pounds and sell it for $1.25 $ ⁢ 1.25 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

Answer:

1st candy: 19.83 pounds,

2nd candy: 5.17 pounds.

Step-by-step explanation:

Let x represent pounds of 1st candy and y represent pounds of 2nd candy.

We have been given that grocer wants to mix a total of 28 pounds. We can represent this information in an equation as:

$x+y=28...(1)$

$y=25-x...(1)$

We are also told that one kind sells for $1.10 per pound, and the other sells for $2.55 per pound. He wants to mix a total of 28 pounds and sell it for $1.25 per pound. We can represent this information in an equation as:

$1.10x+2.55y=28(1.25)...(2)$

Upon substituting equation (1) in equation (2), we will get:

$1.10x+2.55(25-x)=28(1.25)$

$1.10x+63.75-2.55x=35$

$1.10x-2.55x=35-63.75$

$-1.45x=-28.75$

$x=\frac{-28.75}{-1.45}$

$x=19.827586\approx 19.83$

Therefore, the grocer should mix approximately 19.83 pounds of 1st candy.

Now, we will substitute $x=19.83$ in equation (1) to solve for y as:

$y=25-19.83$

$y=5.17$

Therefore, the grocer should mix approximately 5.17 pounds of 2nd candy.