problem solving 3. question 19

Okay so yesterday in math class, we got the grade 10 Canadian Mathematics Contest from 2006. I came in late so I had to rush through all the questions, but there was one that stood out to me as both challenging and fun. I liked it because it was a little bit confusing and I almost got it wrong the first time because I read it wrong. From this I learned that I always have to read the questions very carefully and make sure I understand what they are asking. The question was number 19.

19. In a bin at the Cayley Convenience Store, there are 200 candies. Of these candies, 90 % are black and the rest are gold. After Yehudi eats some of the black candies, 80 % of the remaining candies in the bin are black. How many black candies did Yehudi eat?

a) 2
b) 20
c) 40
d) 100
e) 160

At first when I looked at this question, I automatically assumed that the answer was 20. Then I saw that in the question, it stated that 80% of the REMAINING candies were black. I then looked at the multiple choice answers given to you. I knew the answer wasn't a) 2, because the number is way too small. I also knew that b) 20 was wrong now, and so I tried out c) 40, to see if it worked out.

If 90 % of the 200 were black at the beginning, then that means that 180 of them were black.

200 x 0.9 = 180

If I take away c) 40, then I am left with 140 black candies and 20 gold candies,

200 - 180 = 20

and this is obviously not 80%.

140/160 = 0.875 = 87.5%

All of a sudden, the answer was really obvious. I didn't even have to look at the next multiple choice answer to know that the answer was d) 100. If I take away 100 from 180, then I am left with 80 black candies, and 20 gold candies, which works out to be the answer.

180 - 100 = 80

80/100 = 0.8 = 80%

The answer is d) 100