Applying percent error with an underestimate
About this video
Lina estimated 132 people, which was a 25% underestimate. Letting A be the actual attendance, the video writes A − 0.25A = 132, so 0.75A = 132 and A = 132 ÷ 0.75 = 132 × 4/3 = 176.
You'll be able to
- decide whether the actual value is more or less than an estimate.
- write an equation for an underestimate: A − 0.25A = estimate.
- solve 0.75A = 132 by dividing, or by multiplying by 4/3.
Key words
- Underestimate
- A guess that is smaller than the actual amount.
- Percent error
- How far off an estimate is, as a percent of the actual value.
- Reciprocal
- Flipping a fraction; dividing by 3/4 is the same as multiplying by 4/3.
Transcript
- [Instructor] "Lina estimated 132 people would attend the wheelchair basketball championship. This was an underestimate by 25%. How many people actually attended the wheelchair basketball championship?" Pause this video and try to solve that. All right. So the first thing, just to do a reality check.
is we saw that the estimate is an underestimate by 25%. So the actual number is going to be more than that. And then the next thing to think about is how is this percent error actually calculated? And we know it's an underestimate. So let's just say A is equal to the actual number that attended.
So if we take the actual number and then from that we were to subtract 25%, the percent error. And I'll write that as a decimal, 0.25 times the actual. Then this is going to be equal to what our estimate is. How did I know to subtract 0.25? Well, they tell us that the estimate was an underestimate, so that's why I'm subtracting.
If they said it was an overestimate, I would have added over here. And so another way to think about this, if this is 1a - 0.25a, this is 0.75a is equal to, our actual estimate, is equal to 132. I could just divide both sides by. Actually, let me just do that first.
Both sides by 0.75, both sides by 0.75. And so I get A is equal to this. A is equal to 132 over 0.75. Now, let's see, to calculate that, that's 132 over 0.75 is the same thing as 3/4. If you divide by 3/4, that's the same thing as multiplying by 4/3. So this is the same thing as 132 over 1 times 4 over 3.
And let's see, this, I could use a calculator, but I don't want to. I see the 132, it is divisible by three. If I add up its digits, it's digits, the sum is divisible by three. So let me see. 3 goes into 132. 3 goes into 13 four times. 4 times 3 is 12, subtract, and we get 12.
3 goes into 12 four times. 4 times 3 is 12, and we get no remainder. So another way to think about it is this is 44 times 3 times 4 over 3. We can divide the numerator and the denominator by three. So this is all going to simplify to 44 times 4. So it's equal to 44 times 4, which is, let's see, that's going to be 160 + 16.
40 times 4 is 160. 4 times 4 is 16, which is equal to 176. And we can just do a reality check here. Lina estimated 132. That does look like an underestimate when we compare it to this actual that we calculated. And we are all done.
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