A recipe for fruit punch calls for cranberry juice and sparkling water. The ratio of cups of cranberry juice to cups of sparkling water is 6:24. According to the recipe, how many cups of cranberry juice are needed for every 1.5 cup of sparkling water? Write your answer as a fraction in simplest form.

x=3/8

Correct!

So the answer is 3/8.

To find out how many cups of cranberry juice are needed for every 1.5 cups of sparkling water, we need to determine the ratio between the two ingredients.

The given ratio is 6:24, which means for every 6 cups of cranberry juice, there are 24 cups of sparkling water. To convert this ratio into a simpler form, we can divide both numbers by their greatest common divisor, which is 6 in this case.

Dividing 6 and 24 by 6, we get a simplified ratio of 1:4. This means that for every 1 cup of cranberry juice, we need 4 cups of sparkling water.

Since we want to find out how many cups of cranberry juice are needed for every 1.5 cups of sparkling water, we can multiply both parts of the ratio by 1.5.

1 x 1.5 = 1.5
4 x 1.5 = 6

Therefore, for every 1.5 cups of sparkling water, we need 1.5 cups of cranberry juice. We can write this as the fraction 1.5/6, which simplifies to 1/4 in its simplest form.

So, according to the recipe, you would need 1/4 cup of cranberry juice for every 1.5 cups of sparkling water.

6/24 = x/1.5

Cross multiply and solve for x.