Need help finding the range of possible measurement

Question

Using a scale, jeremy correctly found the mass of a toy car to be 2500 grams. karen and Anna used different scales and recorded different masses for the same toy car. the percent error in karens measurement was at most 5% and annas was at most 3%. What is the range for Karen's possible measurement? Would 10 be correct?

Answer 1

Remember, "range" refers not to a single number, but to a set of numbers, from lowest to highest. If Karen's & Anna's measurements had some percentage of error, that error could be lower or higher than the correct measurement (notice the words "at most"). You should assume that Karen's measurement could be any amount 5% lower than correct up to 5% higher than correct. Likewise, Anna's measurement would be 3% lower up to 3% higher than correct. These are your ranges.

 

Now, what is the "correct" measurement? This problem states that Jeremy measured the mass correctly at 2500 grams, so we can only assume that Karen's measurement was somewhere between 5% lower up to 5% higher than 2500 grams & Anna's measurement was between 3% lower up to 3% higher than 2500 grams.

 

This problem refers to "different scales", but gives no further information about these scales. We also do not know if these two girls used a scale different than Jeremy's or if they used scales different than one another. Without further information, we must assume that such information is irrelevant. We must also wonder why this problem mentions Anna at all, as it does not ask us to determine anything regarding her measurements. It looks to me like we can just ignore Anna altogether - perhaps she was included to throw you off!

 

So, let's get to it & solve the problem with the information we do know. As "percent" refers to some portion of something, we have to understand to what it refers - in this case, it refers to the correct measure, 2500 grams:

 

(2500 grams) - 5%(2500 grams) is the lowest possible measurement Karen will make because we subtract 5% of 2500 from the correct measure, 2500 grams.

 

(2500 grams) + 5%(2500 grams) is the highest possible measurement Karen will make because we add 5% of 2500 to the correct measure.

 

These two measurements define the range of Karen's possible measurements, and Karen's measurement could be any number within that range - i.e. between those two measurements, inclusive of those defining points.

 

Now, some computations:

5%(2500 grams) = 1/20 x 2500 grams = 2500/20 = 125 grams

2500 grams - 125 grams = 2375 grams

2500 grams + 125 grams = 2625 grams

 

When talking about range, we would say, "2500 grams, plus or minus 125 grams" or "2500 grams, give or take 125 grams". Does this make sense to you?

 

Karen's range of possible measurements is 2375 grams to 2675 grams. Her measurement could be any number within that range, including 2375 & 2625. A mathematical way of writing this would be:

 

2375<=X<=2625