Answer:
1.
[tex]\dfrac{3}{7}\ \text{cup of concentrate}\\ \\\dfrac{4}{7}\ \text{cup of water}[/tex]
2.
[tex]\dfrac{2}{3}\ \text{cup of concentrate}\\ \\\dfrac{4}{3}\ \text{cups of water}[/tex]
Step-by-step explanation:
Mix Y:
6 cups of concentrate + 8 cups of water
The ratio of concentrate to water is [tex]\dfrac{6}{8}=\dfrac{3}{4}=3 : 4[/tex]
Suppose you were making only 1 cup of mix Y.
Then
Amount of concentrate = 3x cup
Amount of water = 4x cup
Altogether = 1 cup,
[tex]3x+4x=1\\ \\7x=1\\ \\x=\dfrac{1}{7}\\ \\3x=\dfrac{3}{7}\ \text{cup of concentrate}\\ \\4x=\dfrac{4}{7}\ \text{cup of water}[/tex]
Mix W:
3 cups of concentrate + 6 cups of water
The ratio of concentrate to water is [tex]\dfrac{3}{6}=\dfrac{1}{2}=1 : 2[/tex]
Suppose you were making 2 cups of mix Y.
Then
Amount of concentrate = x cups
Amount of water = 2x cups
Altogether = 2 cups,
[tex]x+2x=2\\ \\3x=2\\ \\x=\dfrac{2}{3}\ \text{cup of concentrate}\\ \\2x=\dfrac{4}{3}\ \text{cups of water}[/tex]
