To receive a B in his chemistry class, Mateo needs to earn an average score from 80 to 89, inclusive. His grade is based only on 3 tests. The highest possible score on each of these tests is 100 points. He scored 79 on his first test and 95 on his second test. If y represents his score on the third test, which of the inequalities below shows all values of y that would earn Mateo a B in his chemistry class?
A. 66 ≤ y ≤ 93
B. 66 ≤ y ≤ 100
C. 80 ≤ y ≤ 89
D. 80 ≤ y ≤ 93
Answer:A
To receive a B in his chemistry class, Mateo needs to earn an average score from 80 to 89, inclusive. His grade is based only on 3 tests. The highest possible score on each of these tests is 100 points. He scored 79 on his first test and 95 on his second test. If y represents his score on the third test, which of the inequalities below shows all values of y that would earn Mateo a B in his chemistry class?
A. 66 ≤ y ≤ 93 B. 66 ≤ y ≤ 100 C. 80 ≤ y ≤ 89 D. 80 ≤ y ≤ 93
Explanation: A Total score = average score × the number of tests. In order for Mateo to receive a B, he needs his total score over the 3 tests to be between 3 × 80 = 240 points and 3 × 89 = 267 points. On his first and second tests, Mateo scored a total of 79 + 95 = 174 points. Therefore, on his third test Mateo must score between 240 - 174 = 66 and 267 - 174 = 93 points in order to receive a B. The correct answer is (A).