what score did he receive on his first exam?

Question

Scott showed improvement on his five math exams throughout the semester improving by 3% on each successive exam. If the 5th exam counted twice as much as the first four exams and his average was a 79% for all five exams, what score did he receive on his first exam?

Answer 1

s represents score on first test

1.03(s) represents score on the second test

(1.03)(1.03)(s) represents score on third test

(1.03)(1.03)(1.03)(s) represents score on fourth test

(1.03)(1.03)(1.03)(1.03)s represents score on fifth test

 

Simplifying

s represents score on first test

1.03s represents score on second test

1.0609s represents score on third test

1.092727s represent score on fourth test

1.12550881s represents score on fifth test

 

Now to the average. The fifth score is "twice as much as the first four."

This means that a total of 12 scores are used - the first 4 and the 2(4) for the fifth.

 

The sum of the first four

5.30913581s

 

Eight times the fifth

8(1.12550881)s

9.00407048s

 

The sum of the 12 test scores

14.3132063s

 

14.3132063s = 12(79)

14.3132063s = 948

s ≈ 66.2325394

 

The score on the fifth exam was approximately

1.12550881(66.2325394)

74.5453

 

This number is less than the average. I need some time to go over my calculations.