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High school math problem

I have 42 coins. The sum of my 42 coins equal to a dollar exactly. I have at least a quarter, a dime, a nickel, and a penny. How many dimes and nickels do I have?

a)3
b)4
c)5
d)6
e)7

February 8, 2016

8 Comments • Newest first

death00

I haven't done logic problems like this in the longest time lol (college senior studying Biology here).
But this is how I solved it:

You know you have at least one of each coin, which adds up to $0.41 in 4 coins already.
$1.00 - $0.41 = $0.59

Since there are 42 coins total, you must make up this $0.59 in the remaining 38 coins.

I started by assuming a case where all 38 coins were pennies, valued at $0.38.

Then you start by looking at 'replacement values' of each coin; A quarter's replacement value is $0.24, i.e. replacing a penny with a quarter results in a net +$0.24. Thus, adding even one quarter can obviously be discounted right off the bat because $0.38 + $0.24 = $0.62, which is greater than the $0.59 we must make up.

It follows that the replacement values for the other coins are as follows:
Dime = $0.09
Nickel = $0.04

We must make up a $0.59 difference, which is off from the all-penny case of $0.38 by exactly $0.21

So which combination of additional dimes and nickels, replacing a penny each time, adds up to $0.21?
1 dime and 3 nickels; 1($0.09) + 3($0.4) = $0.21

So our $0.41 difference is made up of 1 dime, 3 nickels, and 34 pennies.

But remember, we started with one of each coin at the beginning (our initial $0.41)
So in the end, we have:
1 Quarter
2 Dimes
4 Nickels
35 Pennies

1($0.25) + 2($0.10) + 4($0.05) + 35($0.01) = $1.00

Dimes + Nickels = 6

Reply February 9, 2016 - edited
Juxos

@wontpostmuch: ohlol i didnt read the beginning but still easy

Reply February 9, 2016 - edited
MrSatan

69 (sixty nine)

Reply February 9, 2016 - edited
xXjarakudaXx

1 Quarter
2 Dimes
4 Nickels
35 Pennies
So 6?

Reply February 9, 2016 - edited
WontPostMuch

@juxos: LOL what?? They can't all be right. If you have just 3 of dimes and nickels, then at best you have $.20 cents. Add a quarter and you have $.45. You need more than 50 pennies to make a dollar so clearly this can't be the answer since you have 42 coins.

I did find the wording to be problematic though. Makes it seem like you have 3 dimes and 3 nickels instead of 3 coins of nickels and dimes combined.

Reply February 9, 2016 - edited
Samygxz85

ok im not quite sure about this, i know a quarter is 25, a penny is 1, im guessing dime and nickel are 10 and 5? without this i cant solve the problem and i wont cuz if its not like that ill have to do it again haha

Reply February 9, 2016 - edited
Renni

25+10+5+1 = 41 -> 4 coins
+34(1) = 75 -> 38 coins
+1(10)+3(5) = 100 -> 42 coins
so 1+1+3+1 = 6 dimes & nickels?

Reply February 8, 2016 - edited
Juxos

Highschool? ummm this is like 4th grade math o.o
Also there isn't really a right answer, they all could be right -_-

Reply February 8, 2016 - edited