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.)

Question

GPT-4o mini · Answer

To calculate Chelsea's percent error, we can use the formula for percent error:

\[ \text{Percent Error} = \left( \frac{|\text{Actual Value} - \text{Guess}|}{\text{Actual Value}} \right) \times 100 \]

For Chelsea:

Actual Value = 87
Guess = 85

Calculating Chelsea's percent error:

\[ \text{Percent Error} = \left( \frac{|87 - 85|}{87} \right) \times 100 = \left( \frac{2}{87} \right) \times 100 \approx 2.3% \]

So, Chelsea's guess of 85 plastic animals had a percent error of 2.3%.

For Aziz, we know that his percent error is 5%. We can use the same formula:

Let \( x \) be Aziz’s guess. Given that the actual value is 760 gumballs and the percent error is 5%, we can set up the equation:

\[ 5 = \left( \frac{|760 - x|}{760} \right) \times 100 \]

Simplifying this equation:

\[ 0.05 = \frac{|760 - x|}{760} \]

\[ |760 - x| = 0.05 \times 760 = 38 \]

This gives us two possibilities for \( x \):

\( 760 - x = 38 \) → \( x = 760 - 38 = 722 \)
\( 760 - x = -38 \) → \( x = 760 + 38 = 798 \)

Therefore, Aziz could have guessed either 722 gumballs or 798 gumballs.

Now we fill in the required sentences:

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%.

(Place the smaller of the guesses in the first box: 722.)