Hi! Welcome to Math Antics. In our last lesson about percents,
we learned that there’re three main types of percent problems because there’s three different numbers that could be missing.
Those three numbers are the ‘part’, the ‘total’, and the ‘percent’.
They’re just the three variable (or changeable numbers) in the percentage equation.
The forth number is always 100, since that’s what percent means: per 100.
In the last two videos, we learned how to solve problems where the ‘part’ was unknown and where the ‘percent’ was unknown.
In this video, we’re gonna learn how to solve problems where the ‘total’ is unknown or missing.
With this type of problem, you’ll be told what the percent is,
and you’ll be told what part of the total you have.
But you’ll need to figure out what that total itself is.
Here’s an example of a problem like that:
Your friend has a bag of marbles, and he tells you that 20% of the marbles are red.
If there’s 7 red marbles,
how many marbles does he have altogether?
Okay, so how do you know that it’s the total that’s missing in this problem?
Well, the word “altogether” is a big clue because it means almost the same thing as “total”.
So, if the question has words like, “altogether”, or “in all”, or “total”, or “whole”, or “entire”
those can help you know that you need to find the total.
And another way that we can tell is by the numbers that we ARE given.
In this problem, we know that the percent is 20, and we’re also told that PART of the marbles are red,
so we know that the PART is 7.
So that means that it must be the total that’s missing!
Alright then, so how do we figure out what the total is?
Well, using a little algebra (which you don’t need to know how to do right here)
we can re-arrange our percent equation like this:
What this new form of the equation tells us is that,
if we take the ‘part’ and multiply it by 100, and then we divide that by the ‘percent’, we’ll get the ‘total’.
That seems simple enough. It’s just two steps!
Let’s try it out on our word problem about the marbles.
We know that the ‘part’ (that are red) is 7,
so step one is to just multiply that part by 100.
7 × 100 is 700.
And in step two, we take that 700 and divide it by the ‘percent’, which we’re told is 20.
Okay, 700 divided by 20…. hmmm….
Well, we could use a calculator to divide, but this doesn’t seem too hard,
so I’ll just do the division the long way.
20 is to big to divide into the first digit (7) so we’ll need to include the digit next to it as well.
Now we ask, “How many ’20’s does it take to make 70 or almost 70”.
That would be 3 because 3 × 20 is 60.
70 minus 60 leaves 10 as the remainder.
And then we bring down the zero and then we ask, “How many ’20’s will divide into 100?”
Ah-ha… 5, because 5 × 20 is 100, so that leaves no remainder.
So 700 divided by 20 is 35.
And that means that the total number of marbles is 35.
And in a problem like this, you can always check your answer
by making sure that the fraction of the ‘part’ over the ‘total’ would give you the correct percent.
For example, in this case, you could make sure that the fraction 7 over 35 would really be 20%.
Now that wasn’t so tough, was it?
Let’s see one more example to make sure you’ve got the procedure down before you try some on your own.
The next problem says:
A high school marching band has 12 flute players.
[frantic flute music]
If 8% of the band members play the flute,
then how many members are in the entire band?
Okay, so the smaller ‘part’ in this problem is 12 since there’s 12 flute players.
And we’re told that they make up 8 percent of the band, so the ‘percent’ is 8.
Again, it’s the ‘total’ that’s missing,
and to find it, we just need to follow our 2-step procedure.
For step one, we multiply the ‘part’ by 100:
12 × 100 = 1,200
For step two, we divide that 1,200 by the percent, which is 8.
(This time I think I’ll use a calculator to divide.)
1,200 divided by 8 equals 150.
Great… that means that the total number of band members is 150.
And again, you can always check your answer the way we did in the last example.
Alright… that does it for this lesson.
Remember… the key to getting really good at math is to do it yourself.
Doing practice problems on your own will help you become a great problem solver.
Good luck! Thanks for watching Math Antics and I’ll see ya next time.
Learn more at www.mathantics.com
