Amelia had 209 dollars in her bank account. She wrote checks for 95 dollars, 69 dollars, and 86 dollars and made two deposits of 22 dollars and 79 dollars. Determine the amount of money she had after these transactions, and find out how it compares to the original balance.
There’s a lot going on in this problem, so let’s read it again carefully and think about what we can do to solve it. To begin with, we’re told that Amelia had 209 dollars in her bank account. We call this amount her balance. And like any bank account, we can have money coming into the bank account, so the balance increases. And we can have money going out the bank account, so the balance decreases. As we read the problem, we can see that Amelia has both money coming in and out.
When we make a deposit into a bank account, we put money in. And so, we can see that Amelia puts in two amounts of money, 22 dollars and 79 dollars. But we can also see that Amelia takes money out of her account. When we write a check for something, this means we pay for something, and money gets transferred out of our bank account to someone else. So, in a way, Amelia is spending money. She spends 95 dollars, 69 dollars, and also 86 dollars.
And our question asks us to find two pieces of information. Firstly, we need to calculate the amount of money Amelia had after the transactions, in other words, after all her deposits had gone in and all her checks had come out. Secondly, we need to compare this amount to the amount of money she started with, her original balance. Now, there are several steps to this problem, and drawing a bar model is quite tricky for this one. But let’s work through it slowly and see how it can help us.
To begin with, we can calculate the amount of money that Amelia has. We know she starts off with 209 dollars. And we know that the two deposits that she puts into her account are worth 22 dollars and also 79 dollars. Now, if we add these three numbers together, this will give us the total amount of money that Amelia has. Firstly, let’s add the ones, nine plus two plus nine. We know that double nine is 18. And if we have the two as well, this takes us to 20 ones. We can’t write 20 in the ones place, but we can exchange our 20 ones for two tens.
Next, we can add our tens digits. Zero plus two plus seven equals nine. We’ve also exchanged two tens as well. This takes us to 11 tens. We can exchange 10 of our 11 tens for 100. So, we can write the answer as 100 and one 10. Finally, if we add the digits in the hundreds column, we have 200 at the top and 100 that we’ve just exchanged, which takes us to 300. So, the money that Amelia started with plus her two deposits comes to a total of 310 dollars.
Let’s complete the top bar of our bar model to represent this amount. It makes the problem a little clearer. Now, to find the amount of money that Amelia has after all her transactions, we need to subtract all the checks she wrote. We could subtract 95 and then 69 and then 86. Or we could add all three together and then just perform one subtraction. Let’s try this second method.
So, we need to add 95, 69, and 86. When we’re adding three digits like this, sometimes it’s useful to find ways to pair them up. For example, if we look at the ones, if we add five and six together, we get 11. And then, we can add nine easily to get a total of 20. Just like before, we can exchange our 20 ones for two tens. Now, we can combine our tens digits together. We have nine, six, eight, and the two we exchanged. Well, we can see that we can combine the eight and the two to make 10. And we know that nine and six make 15. And if we add 15 and 10 together, we get a total of 25.
This is the same as two hundreds and five tens. There are no hundreds to write in the hundreds place, apart from the two that we’ve exchanged. And so, we can say that the total amount of money that Amelia takes out of her account by writing checks is 250 dollars. So, the amount of money that Amelia will have left after all of her transactions will be this value here. And the way to find it is to subtract 250 from 310.
We know the difference between 31 and 25 is six. And so, the difference between 31 tens and 25 tens is six tens. 310 take away 250 equals 60. So, the amount of money that Amelia has left after all her transactions is 60 dollars. Remember that we have one more part of the problem to solve; we need to find out how this number, 60 dollars, compares to the original balance. In other words, what’s the difference between 60 and 209?
Well, we know that 60 is going to be less than 209, but how much less? Let’s start with 209 and count backwards. We can make a small jump, to start with, of nine. This will take us from 209 to around number 200. Then, we can make a larger jump of 100. This will take us to 100 itself. And now, we need to get from 100 to 60. And we can do this by making a final jump of 40. We’ve made jumps of nine, 100, and 40. So, the difference between both amounts is 149.
We’ve had to complete several steps to get to this answer. Amelia started with 209 dollars. She wrote checks for 95 dollars, 69 dollars, and 86 dollars and made two deposits of 22 dollars and 79 dollars. Her current balance is 60 dollars. And it is 149 dollars less than the original balance.