For this item, any answer that is not a whole number should be entered as a decimal, rounded to the nearest tenth.
The school library is having a competition for the book fair. Students must guess the number of plastic animals in a large jar, or the number of gumballs in another large jar. The students with the closest guess for each jar will win a free book.
Chelsea had the closest guess of 85 for the plastic animals, which actually had 87 plastic animals in the jar. Aziz had the closest guess with an error of 5% for the gumballs, which actually had 760 gumballs in the jar.
Use the given information to complete the following sentences.
Chelsea's guess of 85 plastic animals had a percent error of
%.
Aziz's guess must have been
gumballs or
gumballs since his guess had a percent error of 5%. (Note: place the smaller of the guesses in the first box.)
Chelsea's guess of 85 plastic animals had a percent error of 2.3%.
Aziz's guess must have been 722 gumballs or 798 gumballs since his guess had a percent error of 5%. (The actual value could be either 722 or 798, depending on whether Aziz's guess was too high or too low.)
Chelsea's guess of 85 plastic animals had a percent error of 2.3%.
Aziz's guess must have been 722 gumballs or 798 gumballs since his guess had a percent error of 5%. (Note: place the smaller of the guesses in the first box.)
To find the percent error for Chelsea's guess, we can use the formula:
Percent Error = (|Actual Value - Estimated Value| / Actual Value) * 100
In this case, the actual value of plastic animals in the jar is 87 and Chelsea's estimate is 85. So, the percent error can be calculated as:
Percent Error = (|87 - 85| / 87) * 100
Percent Error = (2 / 87) * 100
Percent Error ≈ 2.3%
Therefore, Chelsea's guess of 85 plastic animals had a percent error of approximately 2.3%.
To find the possible range for Aziz's guess for the number of gumballs, we can use the percent error information. Since his percent error was 5% and the actual number of gumballs is 760, we can set up the following equation:
5% = (|760 - Estimated Value| / 760) * 100
To solve for the estimated value, we can rearrange the equation:
|760 - Estimated Value| / 760 = 5% / 100
|760 - Estimated Value| / 760 = 0.05
Next, we can remove the absolute value by considering both positive and negative scenarios:
760 - Estimated Value = 760 * 0.05
Estimated Value - 760 = 760 * (-0.05)
Simplifying the equations gives us:
760 - Estimated Value = 38
Estimated Value - 760 = -38
Solving both scenarios:
Estimated Value = 760 - 38 = 722
Estimated Value = 760 - (-38) = 798
Therefore, Aziz's guess must have been either 722 gumballs or 798 gumballs since his guess had a 5% percent error.