Maths Olympiad Prep

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Algebra Difficulty 3.1 AMC 10/12 Find the answer

A large bag of coins contains pennies, dimes and quarters. There are twice as many dimes as pennies and three times as many quarters as dimes. An amount of money which could be in the bag is

Pick one

Solution

Let there be xx pennies. Therefore, there are 2x2x dimes and 3(2x)=6x3(2x)=6x quarters. Since pennies are 0.01$, dimes are 0.10,andquartersare, and quarters are 0.250.25, the total amount of money is 0.01x+(2)(0.10x)+(6)(0.25x)=0.01x+(2)(0.10x)+(6)(0.25x)=1.71x1.71x. Therefore, any amount of money must be a multiple of 1.71$. Since the answer choices are all whole dollar amounts, we multiply by $100$ to get a whole dollar number: 171.Noticethattwicethisis. Notice that twice this is 342342, which is answer choice C\boxed{\text{C}}.

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.