Question

2. To get to the semi finals, a dancer has to score at least an average of 8 points. There are 4 judges in the

competition. The first three judges gave the dancer 8.9 points, 7.1 points and 8.3 points. What is the lowest
score 4th judge can give this dancer in order for her to move to the semi finals? Show all your work and justify
all your steps. You will not receive credit unless you justify the step. Please be sure to answer the question.

Answer 1

The lowest score 4th judge can give this dancer in order for her to move to the semi finals is 7.7.

Explanation:

Let x points be the score that 4th judge gave to the dancer.

The first three judges gave the dancer 8.9 points, 7.1 points and 8.3 points.

In total, the dancer got

`8.9+7.1+8.3+x=24.3+x` points

The average score is

`(24.3+x)/(4)`

This average score must be at least of 8 points, so

`(24.3+x)/(4)\ge 8\\ \\24.3+x\ge 32\\ \\x\ge 32-24.3\\ \\x\ge 7.7`

The lowest score 4th judge can give this dancer in order for her to move to the semi finals is 7.7.