Coin Word Problems - Concept
Setting up a system of equations is usually effective when solving money word problems and word problems involving coins. A knowledge of how to solve systems of equations is necessary to solve these types of equations. Other types of word problems using systems of equations include mixture problems, rate word problems, work word problems and age word problems.
In the United States coins are everywhere, pretty much every home you walk into is going to have like a change drawer or jar or a bowl where people toss their coins at the end of the day. So you guys have a lot of familiarity with working with quarters, nickels and dimes and adding up 25 cents, 10 cents, 5 cents adding up those kinds of denominations. So in the word problems you're going to see, you're going to be given information about the amounts of coins there are and also the values. You're going to want to turn that in 2 equations. For some people it helps them to make a table like this.
I'm going to show you how you might do it, let's juts say you had a problem about quarters and dimes. One of my columns will represent quarters my other column will represent dimes and my third column will represent total. By the way in Algebra class we usually only deal with 2 variables at a time, so although we might in the real world have quarters, dimes and nickels in these problems you're only going to be dealing with 2 of those, you're not going to have all 3 to work with. Okay so my problem here I just made it up it's about quarters and dimes. This first row is going to represent an equation where I'm adding my number of quarters there's a plus sign there to my number of dimes and I'm getting some total number of coins that are in the jar or in the drawer or whatever.
Down here for the value I have to do 25 cents times the number of quarters plus 10 cents times the number of dimes it's going to give me whatever total value the problem presented for me. If this helps you making a table like this by all means please do, if this doesn't help you that's fine too just keep in mind you're going to need 2 equations with 2 variables. One of your equations will be about the amount of coins and the other equations will be about the value of those coins.