Problem solving question: #13

Pure mathematics is, in its way, the poetry of logical ideas. ~Albert Einstein. Math itself could be very challenging but after knowing how to solve the problem you would realize how logical and easy it can be! So here is the question, ok. well you might think this question is pretty easy and I might not be very intelligent enough to solve this right off the bat. -_- Although i think it's more important to learn from your mistakes~ So:


Janet has 10 coins consisting of nickels, dimes, and quarters. Seven of the coins are either dimes or quarters, and eight of the coins are either dimes or nickels. How many dimes does Janet have?

Yesterday, I was stuck in this coin question from the sample of math contest questions part B which I had to email Mr. Cheng for a help. He did reply with a solution and I have realized it was very easy and understandable.

So this is the Solution: We have nickels, dimes, and quarters and there are 10 coins in total. WE do not know how many there are but we do have some clues. Eqation: N+D+Q= 10 coins.
Seven of the coins: D+Q= 7, N+7= 10 N= 3 N+Q= 5
Eight of the coins: D+N = Q+8= 10 Q= 2 = D+5 = 10
D= 5

I'm sorry if I'm not a great explainer at this but once you understand the logic of the question and draw or diagram the question, it is much easier for you to organize and solve the problem. I hope I helped any ways as possible. =)