Kevin and Randy Muise have a jar counting 41 coins, all of which are either quarters or nickles. The total value of the coins in the jar is $5.65. How many of each type of coins do they have?

Answer 1

Alright, math isn't my greatest subject, so I'm not sure about a formula here. Instead, let's use some educated guesswork.

So we have x quarters + y nickels = $5.65

x + y = 41 (Don't be scared about these variables--they're just placeholders for numbers you don't yet know.)

So let's try a few sample numbers. Start with quarters. Let's say we guess there are 15 quarters. This would be $3.75. If we subtract this from $5.65, we're left with $1.90 which is 38 nickels. That would mean 15 quarters + 38 nickels which is 53 coins--much more than 41. The easiest way to reduce the number of coins is to try converting some nickels into quarters.

So now let's try 16 quarters. This is $4.00. That leaves $1.65 in nickels, which is 33 nickels. This puts our coins at 16 + 33 = 49. We're getting closer!

Let's try 17 quarters now. This puts us at $4.25, leaving $1.40 for nickels, which is 28 nickels. That puts us at 17 + 28 which is 45. Noticing a pattern? Each time we add a quarter, we lose 4 coins in our total because 1 quarter = 5 nickels, but we're still including a coin!

Using this pattern, we can see without even having to test that we need one more quarter! But we can test this just to be sure. Now we'll try 18 quarters, which is $4.50. That leaves $1.15 for nickels, which totals 23! 18 + 23 = 41. We've found it!

So your final answer is 18 quarters and 23 nickels are in the jar. Hope that helped! :)