Question

Suppose you were making only 1 cup of mix Y. How much water and how much water and how much concentrate do you need?

Suppose you were making 2 cups of mix W. How much water and how much concentrate do you need?

Answer 1

1.

`(3)/(7)\ \text{cup of concentrate}\\ \\(4)/(7)\ \text{cup of water}`

2.

`(2)/(3)\ \text{cup of concentrate}\\ \\(4)/(3)\ \text{cups of water}`

Explanation:

Mix Y:

6 cups of concentrate + 8 cups of water

The ratio of concentrate to water is
`(6)/(8)=(3)/(4)=3 : 4`

Suppose you were making only 1 cup of mix Y.

Then

Amount of concentrate = 3x cup

Amount of water = 4x cup

Altogether = 1 cup,

`3x+4x=1\\ \\7x=1\\ \\x=(1)/(7)\\ \\3x=(3)/(7)\ \text{cup of concentrate}\\ \\4x=(4)/(7)\ \text{cup of water}`

Mix W:

3 cups of concentrate + 6 cups of water

The ratio of concentrate to water is
`(3)/(6)=(1)/(2)=1 : 2`

Suppose you were making 2 cups of mix Y.

Then

Amount of concentrate = x cups

Amount of water = 2x cups

Altogether = 2 cups,

`x+2x=2\\ \\3x=2\\ \\x=(2)/(3)\ \text{cup of concentrate}\\ \\2x=(4)/(3)\ \text{cups of water}`