Mr. Carter likes to have several cups of coffee and tea throughout the day, but he needs to keep his caffeine intake under the recommended daily limit of 400 milligrams. Each cup of coffee has 96 milligrams of caffeine, and each cup of tea has 47 milligrams of caffeine.
Let c represent the number of cups of coffee and t represent the number of cups of tea. Which pairs (c,t) represent possible amounts of coffee and tea Mr. Carter could have?
Since Mr. Carter needs to keep his caffeine intake under 400 milligrams, we can create the following inequality based on the caffeine content of each cup of coffee and tea:
96c + 47t ≤ 400
Now, let's find the possible pairs (c,t) that satisfy this inequality:
1. If Mr. Carter has 4 cups of coffee and no tea:
96(4) ≤ 400
384 ≤ 400 (This is true)
Therefore, (4, 0) is a possible pair.
2. If Mr. Carter has 3 cups of tea and no coffee:
47(3) ≤ 400
141 ≤ 400 (This is true)
Therefore, (0, 3) is a possible pair.
3. If Mr. Carter has 2 cups of coffee and 2 cups of tea:
96(2) + 47(2) ≤ 400
192 + 94 ≤ 400
286 ≤ 400 (This is true)
Therefore, (2, 2) is a possible pair.
There are more possible pairs that satisfy the given inequality, but these are just a few examples.