On a Mexican holiday - Part 1
On the first day of my holiday, I was at the store and bought a new sombrero for myself, spending half of the money that I had. When I left, I noticed that I had as many cents as I had dollars when I went in, and had half as many dollars as I had cents when I went in.
How much (in dollars) did the sombrero cost?
Note: I had at most 100 coins to start with.
The answer is 49.99.
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
Assume that the number of dollars and cents are \( x \) and \[ y \] respectively, but we calculate will calculate in cents. Based on the question, 100x+y-50x-0.5y=50y+x. 50x+0.5y=50y+x. 49x=49.5y. 98x=99y. Since x and y should be positive integers (the sombero won't be free), therefore x=99 and y=98. Then, the initial money will be $99+$0.98=$99.98 and the sombero will cost $99.98/2=$49.99. *Sorry for bad English..