Final answer:
To maintain an equivalent ratio of sugar to milk when increasing a recipe, multiply both the sugar and milk amounts by the same factor. For example, multiplying by 5 results in a ratio of 15 tablespoons of sugar to 10 tablespoons of milk.
Step-by-step explanation:
If Mark is using a ratio of 3 tablespoons of sugar to 2 tablespoons of milk in a recipe and decides to increase the recipe, we need to maintain the same ratio for any quantity. An equivalent ratio can be found by multiplying both parts of the original ratio by the same number. For example, if Mark wanted to double the recipe, he would use 6 tablespoons of sugar and 4 tablespoons of milk (3 x 2 = 6 and 2 x 2 = 4), keeping the same ratio of 3:2.
To increase the recipe to any desired amount, Mark could use a conversion factor. For instance, if the original recipe makes 1 batch and Mark wants to make 5 batches, he multiplies both parts of the ratio by 5. The new ratio would be 15 tablespoons of sugar to 10 tablespoons of milk, as 3 x 5 = 15 and 2 x 5 = 10. This maintains the sweetness and consistency of the recipe across a larger volume.