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HELP WITH COUNTING

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On my ping-pong team there are four times as many right-handed boys as left-handed boys. Of the students on the team who are left-handed, there are twice as many girls as there are boys. Half of the girls who are on the team are left-handed. If there are 36 people on the team, how many are right-handed boys? (Assume no player plays ping-pong equally well with both hands.)

Mar 13, 2023

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Let's start by representing the number of left-handed boys on the team as `b`. Then, the number of right-handed boys on the team is `4b`, since there are four times as many right-handed boys as left-handed boys.

We are also told that the number of left-handed students on the team who are girls is twice the number of left-handed boys, so we can represent the number of left-handed girls as `2b`.

Half of the girls on the team are left-handed, so the total number of girls on the team is `4b`, since `2b` left-handed girls is half the total number of girls.

Therefore, the total number of boys on the team is `5b`, and the total number of students on the team is `9b`. We are given that there are 36 people on the team, so:

```
9b = 36
b = 4
```

This means there are 4 left-handed boys and 16 right-handed boys on the team.

Mar 13, 2023