Jamie V. answered • 02/27/24
Certified Special Education Teacher with 11+ Years Experience
Hello! This is an example of a classic system of equations problem. You’ll want to set up 2 equations with the given information. One equation is the “value” equation that uses how much each item (in this case coin) is worth and set it equal to the total money. The next equation is the “number of items” equation and set it equal to the number of coins. If you get used to the template, you will start to see the same type of problem over and over again. I’d be happy to explain the other common templates in a tutoring session!
Number of Items and Value Template:
x + y = ___ (total number of items)
_x + _y = ___ (fill in values and then total money)
First, define your variables. Use the question at the end to help you. “How many of each kind does she have?”
x = # of nickels
y = # of quarters
Next, write your 2 equations.
- The total number of nickels and number of quarters should equal all of the coins, so….
x + y = 49
- Use the values of the coins and the total money to make the next equation. Since the total money is written in dollars, you’ll want to change the value of a nickel to 0.05 instead of 5 cents and quarters to 0.25 instead of just 25 cents.
0.05x + 0.25y = 6.05
Then use graphing, substitution, or elimination to solve the system. Because of the decimals, substitution is the easiest method.
Solving by Substitution:
x + y = 49
0.05x + 0.25y = 6.05
Get x or y alone in the first equation. I’ll get y alone by subtracting x on both sides.
y = -x + 49
Now replace -x + 49 for y in the second equation. You should only have x as your variable. Solve for x. Then plug in your answer for x to y = -x + 49. Solve for y.
Your answer for x means there are __ number of nickels and your answer for y means there are __ number of quarters. Always check if your answer makes sense. For example, it wouldn’t make sense to get a fraction or decimal answer here because we can’t have parts of coins.
Good luck!
