It is useful to learn how to solve coin problems as we commonly handle these items in everyday life.
Other similar algebra word problems may involve items with specific values like stamps or tickets.
Examples and solutions of these are shown in Stamp Problems and Ticket Problems
Example 1:
Jane bought a pencil and received change for $3 in 20 coins, all nickels and quarters. How many of each kind are given?
Solution:
Step 1: Set up a table with quantity and value.
|
quantity |
value |
total |
nickels |
|||
quarters |
|||
together |
Step 2: Fill in the table with information from the question.
Jane bought a pencil and received change for $3 in 20 coins, all nickels and quarters.
Let | n = | number of nickels |
q = | number of quarters | |
Total = | quantity × value |
|
quantity |
value |
total |
nickels |
n |
5¢ |
5n |
quarters |
q |
25¢ |
25q |
together |
20 |
300¢ |
Step 3: Add down each column to get the equations
n + q = 20 (equation 1)
5n + 25q = 300 (equation 2)
Isolate variable n in equation 1
n = 20 – q (equation 3)
Substitute equation 3 into equation 2
5(20 – q) + 25q = 300
100 – 5q + 25q = 300
25q – 5q = 300 – 100
20q = 200
q = 10
Substitute q = 10 into equation 1
n + 10 = 20
n = 10
Answer: Jane received 10 nickels and 10 quarters.
Example 2:
John received change worth $13. He received 10 more dimes than nickels and 22 more quarters than dimes. How many coins of each did he receive?
Solution:
Step 1: Set up a table with quantity and value.
|
quantity |
value |
total |
nickels |
|||
dimes |
|||
quarters |
|||
together |
Step 2: Fill in the table with information from the question.
John received change worth $13. He received 10 more dimes than nickels and 22 more quarters than dimes.
Let d = number of dimes.
From the question, work out the relationship between dimes and the other types of coins.
nickels = dimes – 10 = d – 10
quarters = dimes + 22 = d + 22
Total = quantity × value
|
quantity |
value |
total |
nickels |
d – 10 |
5¢ |
5(d – 10) |
dimes |
d |
10¢ |
10d |
quarters |
d + 22 |
25¢ |
25(d + 22) |
together |
1300¢ |
Step 3: Add down the total column to get the equation
5(d – 10) + 10d + 25(d + 22) = 1300
Use Distributive Property and Combine Like Terms
5d – 50 + 10d + 25d + 550 = 1300
5d + 10d + 25d = 1300 + 50 – 550
40d = 800
d = 20
nickels = d – 10 = 10
quarters = d + 22 = 42
Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.