Tan2017 wrote:
In a thoroughly blended mix of chocolate and vanilla, what is the percentage of chocolate by volume?
(1) If 25% more vanilla is added to the mix, volume of the mix becomes 75 fl ox.
(2) If 50% more vanilla is added to the mix, volume of the mix becomes 80 fl ox.
This is an interesting problem. On first glance, at least to me, it looks like the answer
should be E. After all, none of the statements tell you anything about the amount of chocolate outright. It's also interesting that it asks about the
percentage of chocolate, not the
amount of chocolate. That sort of language is something you want to notice - it might signal that there's a trick. In order to be cautious, I'll write out the equations from the question and statements before I make any decisions. The equations look like they'll be pretty simple, so this won't take much time.
Question: what is c/(c+v)?
(1) c + 1.25v = 75
(2) c + 1.5v = 80
If you try to answer the question using just one of those statements, you'll end up with a variable you can't cancel (try it!). But with both statements together, you can use elimination to solve for v:
(c + 1.5v) - (c + 1.25v) = 80-75
0.25v = 5
v = 20
With the value of v, you can also find the value of c, and answer the question.
One final note is that using v and c, rather than x and y, is a good idea - it would be easy to get turned around on what you're solving for if you don't use simple variable names.