There are fifteen children in the gym class who haven't yet been picked to be team leaders. if you need to select four, in how many ways can they be selected?
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aaron2113

06.12.2022

Mathematics

-total number of pumpkins

First witch took $\frac{x-1}{3}$ pumpkins.

The number of pumpkins remained $2\frac{x-1}{3} = \frac{2(x-1)}{3} = \frac{2x-2}{3}$

Second witch took $\frac{\frac{2x-2}{3}-1}{3} = \frac{2x-5}{9}$

The number of pumpkins remained $2\frac{2x-5}{9}= \frac{4x-10}{9}$

Third witch took $\frac{\frac{4x-10}{9}-1}{3} = \frac{4x-19}{27}$

Ghost took 3 pumpkins. The number of pumpkins remained is 3,6 or 9.

Solve equation for each case.

1) $\frac{2x-2}{3}+\frac{2x-5}{9}+\frac{4x-19}{27}+3+3=x$

2) $\frac{2x-2}{3}+\frac{2x-5}{9}+\frac{4x-19}{27}+3+6=x$

3) $\frac{2x-2}{3}+\frac{2x-5}{9}+\frac{4x-19}{27}+3+9=x$

Only equation 2) has a solution which is a whole number: 25

The total number of pumpkins is 25.

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There are fifteen children in the gym class who haven't yet been picked to be team leaders. if you need to select four, in how many ways can they be selected? enter your answer.