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?
a. (2, 4)
b. (1, 7)
c. (0, 8)
d. (3, 3)
We can set up an inequality to represent Mr. Carter's caffeine intake:
96c + 47t ≤ 400
Now we can plug in the pairs of numbers given in the answer choices to see which ones satisfy the inequality:
a. (2, 4): 96(2) + 47(4) = 192 + 188 = 380 (satisfies the inequality)
b. (1, 7): 96(1) + 47(7) = 96 + 329 = 425 (does not satisfy the inequality)
c. (0, 8): 96(0) + 47(8) = 0 + 376 = 376 (satisfies the inequality)
d. (3, 3): 96(3) + 47(3) = 288 + 141 = 429 (does not satisfy the inequality)
Therefore, the pairs that represent possible amounts of coffee and tea Mr. Carter could have are:
a. (2, 4)
c. (0, 8)