Question

Nadia has an average score of 70 after 5 tests. What is the minimum number of tests that Nadia has to score a 100 on to get the average score to at least 89?

Answer 1

Let \(n\) be the number needed. So we want to have
\(5\cdot70+100n\geq 89(n+5)\)
\(350+100n \geq 89n+445\)
\(11n\geq 95\)
\(n\geq 95/11\)
So at least \(n=9\).