Erasers cost 45 cents apiece. Notebooks cost 90 cents apiece. Karla spent $18 for a total of 28 erasers and notebooks. How many notebooks did she buy?

Question

The answer I got is 6 notebooks. However, I still got it wrong. Can someone please explain how I got this question wrong?

Answer 1

With any word problem, start by reading the problem. Ignore any numbers for now. We just want a general understanding of what's going on and what's being asked of us.

Here, we are given the cost of erasers and notebooks. Then we're told someone spent some money buying some of each. We're then asked how many notebooks were bought.

Let's define variables now. Focus on the question at the end of the problem. Usually, that question sets up the number of variables and their definitions. In this case, the question asks us to find the number of notebooks bought. So, use the variable n for notebooks. n = number of notebooks bought

However, there is one other unknown. The number of erasers bought. We'll need to find this as well, So in the same fashion, e = number of erasers bought

n = number of notebooks bought

e = number of erasers bought

Now we reread the problem to create our equations. This time we focus on numbers.

First up is the cost of erasers and notebooks. Erasers are 45 cents, notebooks are 90 cents for a total purchase of 18 dollars

0.45e + 0.90n = 18 $0.45 for each eraser, $0.90 for each notebook, total of $18

Next up, we're told a total of 28 erasers and notebooks were bought

e + n = 28

We now have a system of equations:

0.45e + 0.90n = 18

e + n = 28

Choose your method to solving a system of equations. Substitution probably will be the easiest since at least one variable is by itself.

e + n = 28

e = 28 - n

Substitute this value of e into the first equation

0.45e + 0.90n = 18

0.45(28 - n) + 0.90n = 18

12.6 - 0.45n + 0.90n = 18

12.6 + 0.45n = 18

0.45n = 5.4

n = 12

We could stop here. Karla bought 12 notebooks.

However, let's continue to make sure we got the right answer.

e + n = 28

e + 12 = 28

e = 16

Karla bought 16 erasers. Is this correct though?

Check the answers by plugging e=16 and n=12 into each of our equations, if we get true statements for both equations, we're right.

0.45e + 0.90n = 18

0.45(16) + 0.90(12) = 18

7.2 + 10.8 = 18

18 = 18 TRUE

e + n = 28

16 + 12 = 28

28 = 28 TRUE

So, Karla did but 12 notebooks. She also bought 16 erasers.

Answer 2

Let "e" represent the number of erasers and let "n" represent the number of notebooks. Since the total number of erasers and notebooks is 28, we can say:

e + n = 28 or:

e = 28 - n

When we are trying to determine how much things cost, we can say the number of erasers (e) times $0.45 will be the total amount of money spent on erasers. and the number of notebooks (n) times $0.90 will be the total amount of money spent on notebooks and those two totals added together will be $18.00 so we can say:

0.45e + 0.90n = 18

We can plug in for "28 - n" for "e" to get:

0.45(28 - n) + 0.90n = 18

12.6 - 0.45n + 0.90n = 18

12.6 + 0.45n = 18

0.45n = 5.4

n = 12

If n = 12, then, since e = 28 - n we can say e = 28 - 12 = 16

So the number of notebooks she bought was 12 and the number of erasers was 16

Answer 3

These used to get me, too!

e + n = 28

45e + 90n = 1800

First, solve the 1st equation for one of the variables. I'll do e.

e = 28 - n

Now, since e and 28 - n are equal, we can swap them out for each other.

45(28 - n) + 90n = 1800

1260 - 45n + 90n = 1800

45n = 540

45n/45 = 540/45

n = 12 notebooks

e = 28 - n

e = 28 - 12

e = 16 erasers