Mix W = 5 Cups Concentrate and 8 Cups Cold Water, Mix X = 3 cups concentrate 6 cups cold water, Mix Y = 6 Cups Concentrate 9 Cups cold water, Mix Z = 3 Cups Concentrate 5 cups cold water
Question: If possible, write each comparison of concentrate to water as a ratio. If not possible, explain why.
a. The mix is 60% concentrate.
b. The fraction of the mix that is water is 3/5
c. The difference between the amount of concentrate and water is 4 cups.
I need help with this and I'd be happy if you guys helped me with this :D
A, is 6:4
Of course, I'm here to help! Let's go through each question and determine the ratios for each mix.
a. The mix is 60% concentrate.
To find the ratio of concentrate to water, we need to know the total amount of liquid in each mix. Let's add the cups of concentrate and cold water for each mix:
Mix W: 5 cups concentrate + 8 cups cold water = 13 cups total
Mix X: 3 cups concentrate + 6 cups cold water = 9 cups total
Mix Y: 6 cups concentrate + 9 cups cold water = 15 cups total
Mix Z: 3 cups concentrate + 5 cups cold water = 8 cups total
Now let's calculate the ratio of concentrate to the total liquid for each mix:
Mix W: 5 cups concentrate / 13 cups total = 5/13
Mix X: 3 cups concentrate / 9 cups total = 1/3
Mix Y: 6 cups concentrate / 15 cups total = 2/5
Mix Z: 3 cups concentrate / 8 cups total = 3/8
Looking at the ratios, we can see that none of the mixes have a concentrate-to-water ratio of 60%. Therefore, it is not possible to write any of the comparisons as a ratio of 60% concentrate.
b. The fraction of the mix that is water is 3/5.
For this comparison, we need to calculate the ratio of water to the total liquid for each mix:
Mix W: 8 cups cold water / 13 cups total = 8/13
Mix X: 6 cups cold water / 9 cups total = 2/3
Mix Y: 9 cups cold water / 15 cups total = 3/5
Mix Z: 5 cups cold water / 8 cups total = 5/8
Looking at the ratios, we can see that Mix Y has a water-to-total ratio of 3/5. Therefore, the fraction of the mix that is water is 3/5 for Mix Y.
c. The difference between the amount of concentrate and water is 4 cups.
To determine the difference between the amount of concentrate and water, we subtract the amount of water from the amount of concentrate for each mix:
Mix W: 5 cups concentrate - 8 cups cold water = -3 cups (negative difference, so it's not 4 cups)
Mix X: 3 cups concentrate - 6 cups cold water = -3 cups (not 4 cups)
Mix Y: 6 cups concentrate - 9 cups cold water = -3 cups (not 4 cups)
Mix Z: 3 cups concentrate - 5 cups cold water = -2 cups (not 4 cups)
None of the mixes have a difference of 4 cups between the amount of concentrate and water. Therefore, it is not possible to find a mix with a difference of 4 cups.
I hope this helps you understand how to calculate ratios and compare the amounts of concentrate to water in each mix! Let me know if you have any further questions.