Question

Jody and her friends are playing a game in which the person who scores closest to zero points after three rounds wins! Jody's friend Robyn scored 5 points in the first round, lost 8 points in the second round, and scored 4 points in the third round. Jody scored 10 points in the first round and lost 4 points in the second round. What will Jody need to score in the third round to win the game? (3 points)

Answer 1

Jody needs to lose the third round by 6 points to win the game.

Explanation:

The rule of the game is the person who scores closest to zero points after three rounds win.

Robyn scored 5 points in the first round, lost 8 points in the second round, and scored 4 points in the third round.

So, total points for Robyn = 5-8+4=1

So, the magnitude of the closeness of Robyn's score from zero

=|1-0|=1

Jody scored 10 points in the first round and lost 4 points in the second round.

Let Jody score x point in the third round.

Total points for Jody= 10-4+x=6+x

So, the magnitude of the closeness of Jody's score from zero

=|6+x-0|=|6+x|

The condition for Jody to win the game is his points must be closer to zero than Robyn's points, i.e

|6+x|<1

Case 1: If
`x\geq -6`,

6+x<1

`\Rightarrow x<-5`, which is not possible for this case.

Case 2: If
`x\leq -6`,

-(6+x)<1

`\Rightarrow x+6>1`

`\Rightarrow x>-5`

For this case
`x= -6` is the only possibility.

So, Jody must score -6 in the third round to win the game. i.e Jody needs to lose the third round by 6 points.