Question

Julie is in a singing competition and needs an average score of 9.1 to make it to the next round. There are four judges. The first three judges gave scores of 8.8, 9.5, and 9.2.

What equation can you solve to determine the lowest score the fourth judge can give for Julie to move on?

Answer 1

Solve the equation

`\displaystyle (8.8 + 9.5 + 9.2 + x)/(4) \ge 9.1`,

where
`x` is the minimum score of the fourth judge.

At least 8.9 points.

Explanation:

Let the score of the fourth judge be
`x`.

The average score is the sum of the four judges' score divided by the number of scores. That is:

`\displaystyle \text{Average Score} = (8.8 + 9.5 + 9.2 + x)/(4)`.

The minimum average score needs to be greater than or equal to
`9.1`. In other words,

`\displaystyle (8.8 + 9.5 + 9.2 + x)/(4) \ge 9.1`.

Multiply both sides of by four.

`8.8 + 9.5 + 9.2 + x = 4* 9.1`.

Subtract
`8.8 + 9.5 + 9.2` from both sides of the equation:

`x = 4* 9.1 - (8.8 + 9.5 + 9.2) = 8.9`.

In other words, the minimum score of the last judge is
`8.9` for Julie to move on.