Decora F.

asked • 01/11/20# there are 10 pencils. 6 for 30 cents each and 4 for 25 cents. what is the average price of a pencil?

## 5 Answers By Expert Tutors

Nick A. answered • 01/11/20

(Fully Vaccinated!) Stanford Grad - Math, Science, and Test-Prep Tutor

Hi Decorah!

The average of a set of values is found by adding up all the values and then dividing by how many there are in the set.

If we want to find the average price of a pencil, that means we should first add up how much money it would cost to buy a bunch of pencils and divide by the number of pencils in the bunch.

Here we have 10 pencils.

6 cost $0.30 each. That is $0.30+$0.30+$0.30+$0.30+$0.30+$0.30 = $1.80. We could have also realized that adding 6 of the same value together is the same as multiplying by 6 – in this case, 6 x $0.30 = $1.80.

The other 4 pencils cost $0.25 each for some reason (maybe they're shorter?). All together, those 4 pencils cost 4 x $0.25 = $1.00.

So when we combine the 6 expensive pencils and 4 cheaper pencils, we get a total cost of $1.80 + $1.00 = $2.80.

So now, to find the average price, we need to divide by how many pencils we bought – 10! That would be $2.80÷10 = $0.28.

The average price of a pencil is therefore $0.28, or 28 cents.

We need to consider a few things here. The first thing is the definition of an average with regards to this example. The average price of one pencil is the total cost of all of the pencils divided by the number of pencils.

To find the total price of all ten pencils, we need to multiply 6 times 0.30 (30 cents for each of 6 pencils) and also 4 times 0.25 (25 cents each for 4 pencils). We then need to add these two numbers up and divide that total by 10.

(0.30 • 6 + 0.25 • 4) ÷ 10

(1.80 + 1.00) ÷ 10

2.80 ÷ 10

0.28

This answer also makes sense logically, because the highest price of a pencil is $0.30 and the lowest price is $0.25, so the average should be between those two values, which it is.

I hope that this helps you to understand the question better!

Sydney N. answered • 01/11/20

Math and English Tutor for K-12 Students

6 x .30 = $1.80

4 x .25 = $1.00

Then you add both prices together and divide by 10.

1.80 + 1.00 = $2.80

2.80/10 = $0.28

**The average price is $0.28 for one pencil.**

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