102k views
0 votes
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?

User Lucas Paz
by
6.9k points

2 Answers

3 votes

Answer:

9 dimes

Explanation:

User Goodwinnk
by
6.5k points
3 votes

Answer:

There are 9 dimes in this collection.

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

User Nadavwr
by
7.2k points