To determine the amount of carbohydrates Kate should plan in her meal, we can use the given ratio of carbohydrates to protein to fat, which is 5:2:3.
First, let's calculate the total number of parts in the ratio by adding the three parts together: 5 + 2 + 3 = 10.
Since we know that the meal contains 22g of protein, we need to determine the corresponding amount of carbohydrates.
To do this, we can set up a proportion using the ratio of protein to carbohydrates:
2 parts of protein corresponds to x parts of carbohydrates, where x is the unknown amount of carbohydrates.
The proportion can be set up as:
2/5 = 22/x
To solve for x, we can cross multiply:
2x = 5 * 22
2x = 110
Dividing both sides of the equation by 2 gives:
x = 55
Therefore, Kate should plan 55 grams of carbohydrates in her meal to maintain the recommended ratio of 5:2:3 for carbohydrates, protein, and fat.