How do you solve this?

Question

A student has test scores of 83, 91, and 80, and a homework average of 85 (all out of 100). If the three tests and homework each carry equal weight, and the final exam counts twice as much as a single test, find the range of scores (out of 100) on the final for this student to have an average of at least 80% but less than 90%. Show the set-up of the inequality and its solution.

Answer 1

80 ≤ (83+91+80+85+2x)/6 <90

 

multily all by 6

 

480 ≤ 339 + 2x < 540

 

subtract 339 all through

 

141 ≤ 2x < 201

 

divide through by 2

 

70.5 ≤ x < 100.5

 

Since the scores are all out of 100

 

70.5 ≤ x < 100

 

If all test scores are integers, then

 

71 ≤ x < 100