SOLUTION: a pile of 37 coins consists of nickels and dimes. the total value of the coins is 3.10. find the number of each type of coin

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Question 1139029: a pile of 37 coins consists of nickels and dimes. the total value of the coins is 3.10. find the number of each type of coin
Found 2 solutions by greenestamps, josgarithmetic:
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


(1) Algebra with two variables

n+d = 37 (the total number of nickels (n) and dimes (d) is 37)
5n+10d = 310 (the total value of the coins is 310 cents)

Solve by whatever method you choose.

(2) Algebra with one variable

5n+10(37-n) = 310 (if the number of nickels is n and the total number of coins is 37, then the number of dimes is 37-n)

Solve using basic algebra.

(3) Using logical reasoning and mental arithmetic

> if all 37 coins were nickels, the total value would be 37*5 = 185 cents
> the actual total value is 310 cents, which is 125 cents more than 185 cents
> exchanging a nickel for a dime keeps the total number of coins the same and increases the total value by 5 cents
> the number of nickels to be exchanged for dimes to make the additional 125 cents is 125/5 = 25

So there are 25 dimes and 37-25 = 12 nickels

Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
Simplest way,
x, number of dimes
37-x, number of nickels

0.1x%2B0.05%2837-x%29=3.1------solve for x.
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0.1x%2B1.85-0.05x=3.1
0.05x=3.1-1.85
.
.