Question

Amaya's test scores in Algebra 1 are 78 and 91. She has one more test left and wants to earn a B for the course, which is from 80-89 inclusive. Write a compound inequality to represent the situation

Answer 1

Let x be the score Amaya gets on the final test. She wants her average of all 3 tests to be between 80 and 89: 

80 ≤ (78 + 91 + x) / 3 ≤ 89 

Multiply everything by 3: 
240 ≤ 78 + 91 + x ≤ 267 
240 ≤ 169 + x ≤ 267 

Subtract 169 from everything: 
240 - 169 ≤ x ≤ 267 - 169 
71 ≤ x ≤ 98 

Answer: 
She needs to score between 71 and 98 to get a B for the course.