A collection of dimes and nickels has a total value of two dollars and contains 31 coins. How many dimes are there in the collection?

There are 9 dimes in this collection.

Step-by-step explanation:

Dimes are 10¢; nickels are 5¢.

d + n = 31

0.1d + 0.05n = 2

In this system of equations, d represents the amount of dimes in this collection and n represents the amount of nickels in this collection.

1. Isolate n in the first equation.

n = - d + 31

2. Substitute this value into the other equation to find the value of d.

0.1d + 0.05 (-d + 31) = 2

0.1d - 0.05d + 1.55 = 2

0.05d + 1.55 = 2

0.05d = 0.45

d = 9

If you'd like to know how many nickels are in the collection, just subtract the amount of dimes from the total number of coins in the collection.

31 - 9 = 22