As Halloween approaches, houses are decorated, parties are planned, and many children's minds wander toward their costumes and the haul of candy they're going to collect. Parents' minds typically wander toward the haul of candy they're going to sneak after their children fall into their sugary slumber.
One past Halloween, sisters Cindy and Lisa went trick-or-treating. Cindy was a Viking and Lisa was a Viking cat, which we can only assume involved wearing cat whiskers and a horned helmet. Now Cindy did very well this Halloween, getting more than 100 pieces of candy but less than her all-time record of 200 pieces. Lisa, on the other hand, apparently confused a lot of the homeowners giving out candy, and ended up with just one 3 Musketeers Fun-size bar (not even a full-size one).
Cindy, trying to console her devastated sister, said: "It's not so bad, Lisa! If you take the number of pieces of candy I got, reverse the digits, then add it to the original number, you get the number of calories in your trick-or-treat bag. Well, you would if you had 7 more 3 Musketeers bars."
How many pieces of candy did Cindy get that night?
One past Halloween, sisters Cindy and Lisa went trick-or-treating. Cindy was a Viking and Lisa was a Viking cat, which we can only assume involved wearing cat whiskers and a horned helmet. Now Cindy did very well this Halloween, getting more than 100 pieces of candy but less than her all-time record of 200 pieces. Lisa, on the other hand, apparently confused a lot of the homeowners giving out candy, and ended up with just one 3 Musketeers Fun-size bar (not even a full-size one).
Cindy, trying to console her devastated sister, said: "It's not so bad, Lisa! If you take the number of pieces of candy I got, reverse the digits, then add it to the original number, you get the number of calories in your trick-or-treat bag. Well, you would if you had 7 more 3 Musketeers bars."
How many pieces of candy did Cindy get that night?
So it turns out there are multiple sources for the number of calories in a fun-size 3 Musketeers bar. One works out to 63.33 per bar, and one is just 63 calories per bar. I'm working with the integer 63 as the math works out that way. Sorry for the confusion!
OK, we can do this step by step:
- Cindy collected between 100 and 200 pieces of candy.
- One 3 Musketeers bar is 63 Calories, so if Lisa had 7 more, she would have 8 bars or 504 Calories.
- So if you take Cindy's count, reverse it, then add that to the count, the sum is 504.
- If Cindy's candy count is 100a + 10b + c, then the sum of that and its reverse is 101(a+c) + 20b.
- That suggests that a + c = 4, which suggests that b = 5.
- Because Cindy collected fewer than 200 pieces of candy, a = 1.
- So Cindy now has 153 pieces of candy. And one sad, sad sister.
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