Professor layton and the curious village

Although the hints explain the puzzle fairly well, here's three ways to approach the problem

The question tells us that
a) the total cost of the camera and the case is $310
b) the camera costs $300 more than the case


LOGICALLY

While the puzzle traps many players into initially thinking that the camera costs $300 and the case $10, this doesn't satisfy the condition that the difference in price is $300

As the total price is $310 and the camera must cost over $300 (being the cost of the case plus $300), there's not many possibilities to consider

When you then consider that the cost of the case is the same as the cost of the camera less $300 and that twice this value must add up to $10, the cost of the case must be $5 and the cost of the camera $305


MATHEMATICALLY

camera = case + 300
camera + case = 310

so...

(case + 300) + case = 310
case + case = 10
case * 2 = 10
case = 10 / 2
case = 5


TRIAL AND ERROR

We know that the camera must cost at least $300 (as it costs $300 more than the case) and can not cost more than $310 (being the total cost)

Remembering that the camera costs $300 more than the case, we can work through the possibilities (camera cost + case cost = total cost)

300 + 0 = 300
301 + 1 = 302
302 + 2 = 304
303 + 3 = 306
304 + 4 = 308
305 + 5 = 310 **
306 + 6 = 312
307 + 7 = 314
308 + 8 = 316
309 + 9 = 318
310 + 10 = 320

The only combination where the total of both the camera and the case is $310 is where the camera costs $305 and the case costs $5


CONCLUSION

As you hand over $100 to pay for the $5 case, then you should get $95 in change
http://professorlaytonwalkthrough.blogspot.com/2008/02/puzzle042.html

95 dollars