Mix A=2 cups concentrate:3 cups water
Mix B=5 cups concentrate:9 cups water
Mix C=1 cups concentrate:2 cups water
Mix D=3 cups concentrate:5 cups water
For each mix, how much concentrate and how much water are needed to make 1 cup of juice?
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I will do one of them in a systematic way, you then should be able to reason out the others without any actual work
MIX D
conentrate:water = 3:5
let the amount of concentrate be 3x
and the amount of water be 5x
(notice 3x:5x = 3:5)
then 3x + 5x = 1
8x = 1
x = 1/8
so concentrate = 3x = 3/8 of a cup
water = 5x = 5/8 of a cup
notice how 3/8 + 5/8 = 1
notice 3/8 : 5/8 = 3:5
can you now do the others by observing how the 8 was obtained?
Thanks!!!
A=2/5 & 3/5
B=5/14 & 9/14
C=1/3 & 2/3
If I Determine The Number Of Cups Of Water 1:4 Need And My Friend Mixes 3 Cups Of The Concentrate
Mix A: To make 1 cup of juice, you would need 2/5 cup of concentrate and 3/5 cup of water. Just concentrate on that!
Mix B: To make 1 cup of juice, you would need a whole lot of concentration! Specifically, you'll need 5/14 cup of concentrate and 9/14 cup of water. It's a mix that really knows how to keep it balanced!
Mix C: Time to stay hydrated with Mix C! To make 1 cup of juice, you'll need 1/3 cup of concentrate and 2/3 cup of water. When life gives you concentrate and water, make juicy lemonade!
Mix D: For a refreshing cup of juice, Mix D has got your back! You'll need 3/8 cup of concentrate and 5/8 cup of water. It's the perfect blend to quench your thirst and make you say, "Oh, juice see that!"
To find out how much concentrate and water are needed to make 1 cup of juice for each mix, we can calculate the ratio of concentrate to water for each mix and use it to determine the amounts needed.
Let's start with Mix A:
The ratio of concentrate to water is 2:3. This means that for every 2 cups of concentrate, we need 3 cups of water.
To make 1 cup of juice, we can set up a proportion:
2 cups of concentrate / 3 cups of water = x cups of concentrate / 1 cup of water
Cross-multiplying, we get:
2 cups of concentrate * 1 cup of water = 3 cups of water * x cups of concentrate
2 cups of concentrate = 3 cups of water * x cups of concentrate
Dividing both sides of the equation by 3 cups of water, we find:
2 cups of concentrate / 3 cups of water = x cups of concentrate
Dividing both sides of the equation by 2 cups of concentrate, we get:
1 cup of concentrate / 1.5 cups of water = x cups of concentrate
Therefore, to make 1 cup of juice from Mix A, we would need 1 cup of concentrate and 1.5 cups of water.
Following the same process, we can determine the amounts needed for the other mixes:
Mix B:
The ratio of concentrate to water is 5:9.
Since we want to make 1 cup of juice, the proportions become:
5 cups of concentrate / 9 cups of water = x cups of concentrate / 1 cup of water
Solving for x, we find:
1 cup of concentrate = (5 cups of concentrate * 1 cup of water) / 9 cups of water
1 cup of concentrate = 5/9 cup of concentrate
Therefore, to make 1 cup of juice from Mix B, we would need 5/9 cup of concentrate and 1 cup of water.
Mix C:
The ratio of concentrate to water is 1:2.
Solving for x, we find:
1 cup of concentrate = (1 cup of concentrate * 1 cup of water) / 2 cups of water
1 cup of concentrate = 1/2 cup of concentrate
Therefore, to make 1 cup of juice from Mix C, we would need 1/2 cup of concentrate and 1 cup of water.
Mix D:
The ratio of concentrate to water is 3:5.
Solving for x, we find:
1 cup of concentrate = (3 cups of concentrate * 1 cup of water) / 5 cups of water
1 cup of concentrate = 3/5 cup of concentrate
Therefore, to make 1 cup of juice from Mix D, we would need 3/5 cup of concentrate and 1 cup of water.