Missing Quarters

Algebra Level pending

Annie has a piggy bank full of quarters, her sneaky brother James loves to steal them. He steals 1 on the first day, 2 more on the second day, 3 more on the third, and so on. James is a clumsy kid and loses 1 coin on the fourth day, 2 more on the eighth day, and so on in multiples of 4. How many quarters does he have at the end of the 100th day?

3600 3875 4725 4825

View wiki
Jonathan Dou by Jonathan Dou , 20, USA

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Caleb Townsend
Mar 30, 2015

Triangular number formula: T n = n ( n + 1 ) 2 T_n = \frac{n(n+1)}{2}

The number of quarters stolen is 1 + 2 + 3 + . . . + 100 = T 100 = 50 × 101 = 5050. 1 + 2 + 3 + ... + 100 = T_{100} = 50\times 101 = 5050.

The number of quarters lost is 1 + 2 + 3 + . . . + 25 = T 25 = 13 × 25 = 325. 1 + 2 + 3 + ... + 25 = T_{25} = 13\times 25 = 325.

Therefore the number of quarters he has is 5050 − 325 = 4725. 5050 - 325 = 4725.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

question language not clear

Akash singh - 5 years, 10 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...