This is problem 8 on the grade 11 and 12 Math Kangaroo 2025. Okay, Celia's favorite chocolate bars come in packets. Each packet used to contain five bars. Now they contain only four but are sold at the same price. Truly tragic. By what percentage has the price of each bar increased? Arts choices are A by 10%, B by 20%, C by 25%, D by 30%, and E by 50%. Okay, so we can keep things like we can we can assign a price, but I personally like to keep things generic because, you know, what if the answer changes if we fix something? So then let's like, let's assign some variables. Each packet used to contain five bars. Now they only contain four but are sold the same price. That means we should probably assign a value to the like packets. So same price, let's call that P. So P equals packet price. Packet price. Okay, so yeah, it costs P, maybe dollars. And now let's get like a per bar cost. So the old cost, the old cost was P over five. Because there are five bars and we're sort of assuming they'd be evenly distributed in price because it's the same bars. So each bar costs P over five. But now in the in the new system, we only have four bars. We only have four bars. So by that same logic, each thing is worth P over four. Yeah, awesome. Okay. So now let's actually, you know, do some math. To find the percent increase of something, we sort of need is the difference over like the original. And this can be represented as P over four minus P over five. All over P over five. Doing the work here, we obtain that this is in fact equivalent to, we can, you know, sum these two fractions. 5P over 20 minus 4P over 20 all over P over five. And then this obtains P over 20, all over P over five. And we can represent this thing. Well, we can do multiple things, but let's just like keep change flip, keep it simple. P over 20, you know, divided by P over five means we should, you know, keep this one, change this to a multiplication and then do five over P. And we obtain five over 20 or one over four or 25 percent. Alternatively, we could do this a little bit faster, but just like calling P like 100 or something. If you're, if we're confident that nothing will change. So if P is 100, then each bar costs 20 bucks in the old system. But in the new system, it costs 25 bucks. And like, this is something we probably recognize. It just becomes, you know, five over 20 is 25 percent. So like either way you do it, you can either fix something if you're sort of confident in that, that it won't change. Or you can do it generically with just P and obtain 25 percent either way. But yeah, any way you slice it, it becomes C, 25 percent. Those darn greedy chocolate makers.

chocolate bars

price increase

percentage calculation

cost per bar

packet reduction