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How to Find the Missing Coin

How to Find the Missing Coin
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  • 0:02 A Coin Problem
  • 1:04 Example 1
  • 1:56 How to Solve it
  • 2:33 Example 2
  • 3:15 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Watch this video lesson to learn how you can solve missing coin problems. Learn what mathematical operations you should use to figure out what kind of coin you are missing.

A Coin Problem

In this lesson, we are going to learn how to solve missing coin problems. These are problems where you need to find the value of a needed coin. To help us out, here is Sarah. Sarah works at the local grocery store and it is her job to give people the right amount of change. So, she is very good at solving missing coin problems. She does it all the time when she is at work. Her machine only tells her the total amount of change to give, but it doesn't tell her what kinds of coins she needs to give. It is her job to figure out what kinds of coins are needed. All of this involves finding the missing coin.

Here's Sarah's first customer of the day. The customer needs 7 cents in change. Sarah's gotten two pennies for her customer. What other coin is needed to make 7 cents?

We're trying to answer the question:

1 + 1 + ? = 7

How does Sarah go about finding what kind of coin is needed? Let's see.

How to Solve it

Sarah starts to explain her thought process. She says that what she does is she looks at her total amount of change that is needed and then she starts to subtract the coins she already has from the total. So far, for this customer, she needs to give 7 cents back in change. She already has two pennies, so she subtracts that from the total.

7 - 1 - 1

What does this give her? It gives her 7 - 1 - 1 = 5. So, she needs an additional 5 cents in change. Now that she knows the value of the coin she needs, she can choose the coin that has that particular value. So, what coin has a value of 5 cents? It is the nickel. So, Sarah picks the nickel, and she gives the two pennies and a nickel to the customer. The customer leaves happy.

Sarah has two more customers in line. Let's see how Sarah keeps finding her missing coins.

Example 1

This customer needs 16 cents in change. Sarah starts with a dime and a penny. What other coin does she need?

We're looking for the value that makes this equation true:

10 + 1 + ? = 16

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