Question

A recipe for chocolate caramel milk calls for 6 times as much milk as chocolate syrup and 2/3 as much caramel syrup as chocolate syrup. How much of each should you use to make 3 cups of chocolate caramel milk?

Answer 1

To make 3 cups of chocolate caramel milk, use 1/3 cup chocolate syrup, 2 cups milk, and 2/9 cup caramel syrup.

Explanation:

Let's call the amount of chocolate syrup needed x, then according to the problem statement, we need 6 times as much milk as chocolate syrup and 2/3 as much caramel syrup as chocolate syrup.

So, the amount of milk needed would be 6x, and the amount of caramel syrup needed would be 2/3 x.

We want to make 3 cups of chocolate caramel milk, so the total amount of ingredients would be x + 6x + 2/3 x = 7 2/3 x.

To solve for x, we can set up an equation using the total amount of ingredients:

7 2/3 x = 3

Simplifying, we can multiply both sides by the reciprocal of 7 2/3, which is 3/23:

x = 3/23 * 7 2/3

x = 3/23 * 23/3

x = 1/3

So we need 1/3 cup of chocolate syrup, 6 times as much milk or 6 * (1/3) = 2 cups of milk, and 2/3 as much caramel syrup or 2/3 * (1/3) = 2/9 cup of caramel syrup to make 3 cups of chocolate caramel milk.