7 nickels and 13 dimes
Step-by-step explanation: Let's start this problem by setting up a chart which I have made and provided for you in the image attached.
Down the left side, we will have our different types of coins. In this case, nickels and dimes. Across the top, we ill have our formula. Our formula will be the number of coins we have × the value of each coin = their total value.
Now let's fill out the chart.
For number of nickels and dimes, we know that a person has a total of 20 nickels and dimes but we don't know how many of each they have. In fact, that is what the problem is asking.
So if we represent our number of nickels as x, we can call our number of dimes 20 - x.
The value of each nickel is 5 cents and the value of each dimes is 10 cents.
Our total value based on our formula is going to come from the first column times the second column. So the total value of our nickels is x times 5 or 5x and the total value of our dimes is 20 - x times 10 or 10(20 - x).
Our goal in this problem will be to find x because x represents our number of nickels and the problem asks how many nickels are there. If we know the number of nickels, we can easily find the number of dimes and we will have our final answer but we first need an equation in order to find x and it's important to understand that the information in this equation will always come from the last column of your chart the total value column. So we will be asking ourselves what do we know about the total value of our nickels and the total value of our dimes.
Well we know that the total value of all of our coins is $1.65 so if we add the total value of our nickels + the total value of our dimes, that should equal $1.65.
Below the total value chart, I added another box and I put 165. Notice I wrote $1.65 in terms of cents because our value of nickels and value of dimes is also written in terms of cents and we need to be consistent.
So here is our equation.
5x + 10(20 - x) = 165
I did not show my work for this but the work will be provided in the image attached. When we solve this, we get x = 7.
Going back up into our chart, remember that x represents our number of nickels so the person has 7 nickels.
To get the number of dimes, we take 20 - x which is 20 - 7 or 13 dimes.
So the person had 7 nickels and 13 dimes.
