Simple Mixture
Kane has a solid box that contains litres of alcohol. He drops some amount of water in it, and now the box contains a mixture with an alcohol concentration of .
After the mixture of water, if the total volume of mixture in the box can be expressed as litres (in lowest term), what is ?
The answer is 549.
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
An amount of water is added in the 1 0 litres of alcohol. Let x be the amount of water added.
9 8 % ( 1 0 + x ) = 1 0
9 8 % of the mixture is 1 0 litres of alcohol. The amount of alcohol never changed since we only added water. That gives us with x = 4 9 1 0 .
1 0 + x = 1 0 + 4 9 1 0 = 4 9 5 0 0
The total volume of the mixture inside the box is 4 9 5 0 0 litres, giving us the values for a and b .
a + b = 5 0 0 + 4 9 = 5 4 9