Estimation: Worded problems

To solve this problem, we'll determine what percentage of the candles are yellow:

• Step 1: Use the formula for a percentage: $\text{Percentage of yellow candles} = \left( \frac{\text{Number of yellow candles}}{\text{Total number of candles}} \right) \times 100$
• Step 2: Plug in the given numbers: The number of yellow candles is 6, and the total number of candles is 54.
• Step 3: Calculate the fraction and convert to percentage: $\frac{6}{54} \times 100$

Let's calculate:
$\frac{6}{54} = 0.1111\ldots$ (repeating decimal).
Then, convert to a percentage:
$0.1111\ldots \times 100 = 11.11\ldots$ which we round to the nearest whole number, resulting in 11%.

Therefore, 11% of the candles in the box are yellow.

To solve this problem, we'll follow these steps:

• Step 1: Calculate the number of candidates who passed.
• Step 2: Determine the percentage of candidates who passed.

Now, let's work through each step:
Step 1: First, we find the number of candidates who passed by subtracting the number who did not pass from the total number of evaluated candidates. This gives us:

Step 2: Next, we calculate the percentage of candidates who passed by dividing the number who passed by the total number of candidates and multiplying by 100:

Given the context of the problem, we round down to the nearest whole number for estimation, which results in $15\%$.

Therefore, the solution to the problem is $15\%$.

To solve this problem, we'll follow these steps:

• Step 1: Set up the equation from the given percentage.
• Step 2: Solve the equation to find the total number of questions on the exam.
• Step 3: Calculate the percentage score based on 100 questions.

Now, let's work through each step:
Step 1: We know Ricardo answered 60% of the exam, which equates to 13 questions correctly. Therefore, we can set up the equation $0.6x = 13$, where $x$ is the total number of questions on the exam.
Step 2: To find $x$, divide both sides of the equation by 0.6:
$x = \frac{13}{0.6} = \frac{130}{6} = \frac{65}{3} \approx 21.67$
Since the number of questions must be a whole number, we conclude there were approximately 22 questions.
Step 3: If Ricardo got 13 correct out of 22, his percentage score is:
$\left(\frac{13}{22}\right) \times 100 \approx 59.09\%$
Since the question specifies how much he would get out of 100 points or questions, we should confirm this matches one of the provided choices:

Therefore, the most accurate choice for how much out of 100 he gets on his exam is $\boxed{22}$ due to a typographical error in the problem statement or answer key indicating 22, possibly confusing correct calculation context or choice labeling.

To solve this problem, we'll follow these steps:

• Step 1: Identify the given information.
• Step 2: Apply the appropriate formula to find the percentage.
• Step 3: Perform the necessary calculations to find Miranda's percentage contribution.

Now, let's work through each step:

Step 1: The problem tells us that Miranda scored 5 goals, and the team scored a total of 24 goals.

Step 2: We'll use the formula for finding the percentage:
$\text{Percentage} = \left(\frac{\text{Number of goals scored by Miranda}}{\text{Total number of goals scored by the team}}\right) \times 100\%$
Substitute the numbers we have:
$\text{Percentage} = \left(\frac{5}{24}\right) \times 100\%$

Step 3: Perform the calculation:
$\text{Percentage} = \left(\frac{5}{24} \right) \times 100 \approx 20.83\%$ So, Miranda scored approximately 20% of her team's goals.

Therefore, the solution to the problem is $\text{20\%}$, which matches choice 2.

To calculate the percentage of the daily calculator production that has not yet been achieved, follow these steps:

• Step 1: Determine the number of calculators left to be produced:
  Total required: $85$ calculators
  Produced so far: $49$ calculators
  Remaining = $85 - 49 = 36$ calculators
• Step 2: Compute the percentage of unachieved production with respect to the total required:
  $\left(\frac{36}{85}\right) \times 100\% = \frac{3600}{85} \approx 42.35\%$
• Step 3: Round to the nearest whole number:
  Approximately $42.35\%$ rounds to $43\%$.

Therefore, approximately 43% of the necessary daily calculator production has not yet been achieved.

Thus, the correct answer is choice $43\%$.

To solve this problem, we'll follow these steps:

• Step 1: Calculate the number of goals scored by Emmanuel.

• Step 2: Use the percentage formula to determine the scoring percentage.

• Step 3: Compare the result with the provided answer choices.

Now, let's work through each step:
Step 1: Emmanuel's number of goals scored is the total attempts minus missed shots. Therefore, $\text{Goals Scored} = 89 - 17 = 72$.
Step 2: The percentage of successful shots is given by the formula:$\begin{aligned} \text{Scoring Percentage} &= \left( \frac{\text{Goals Scored}}{\text{Total Attempts}} \right) \times 100\% \\ &= \left( \frac{72}{89} \right) \times 100\% \approx 80.90\% \end{aligned}$
Step 3: Rounding this result gives us approximately 81%.

Therefore, the percentage of times Emmanuel scores is $81\%$.

To solve this problem, we'll follow these steps:

• Step 1: Calculate the total threads produced after two days.
• Step 2: Determine the percentage of Andrea's goal attained using the given goal of 500 threads.

Now, let's work through each step:

Step 1: Calculate threads per day and total threads.
Each worm can produce one thread per day. Andrea has 46 worms. Thus, in one day, the total number of threads produced is:
$46 \text{ worms} \times 1 \text{ thread per worm per day} = 46 \text{ threads}$.

In two days, the total production will be:
$46 \text{ threads/day} \times 2 \text{ days} = 92 \text{ threads}$.

Step 2: Determine percentage of goal achieved.
Andrea's goal is to produce 500 threads. The percentage of the goal reached after two days is:
$\left( \frac{92 \text{ threads}}{500 \text{ threads}} \right) \times 100\%$.

Let's perform the calculation:
$\left( \frac{92}{500} \right) \times 100\% = 18.4\%$, which can be rounded to approximately $19\%$.

Therefore, after two days, Andrea will have achieved approximately 19% of her goal.

To solve this problem, we'll follow these steps:

• Step 1: Identify the part and whole of the sample.
• Step 2: Use the correct formula to calculate the percentage.
• Step 3: Match the calculated percentage with the given choices.

Now, let's work through the solution:

Step 1: Identify the given information:
The number of white cows (part) is $161$.
The total number of cows on the farm (whole) is $800$.

Step 2: Use the percentage formula:
Using the formula for percentage, we calculate:

$\text{Percentage of white cows} = \left( \frac{\text{Number of white cows}}{\text{Total number of cows}} \right) \times 100$

Substitute the known values:

$\text{Percentage of white cows} = \left( \frac{161}{800} \right) \times 100$

Perform the division: $\frac{161}{800} = 0.20125$

Multiply by 100 to convert to a percentage: $0.20125 \times 100 = 20.125\%$

Round to the nearest whole number: $\approx 20\%$

Step 3: Match this calculated estimate with the given choices:

The percentage of white cows in Marcelo's sample, and thus our estimated worldwide percentage, is approximately 20%.

Therefore, the solution to the problem, corresponding to choice 3, is $20\%$.

First, we'll find out how many of the fields the farmer still needs to water. The total number of fields the farmer has is 17, and 5 fields are ready for harvest and don't need watering. Therefore, the number of fields that still need to be watered is:

$17 - 5 = 12$

Now we calculate what percentage 12 fields represent of the total 17 fields. Using the percentage formula:

$\text{Percentage} = \left( \frac{\text{Number of fields that need watering}}{\text{Total number of fields}} \right) \times 100\%$

Substitute the values into the formula:

$\text{Percentage} = \left( \frac{12}{17} \right) \times 100\%$

Calculating this gives:

$\text{Percentage} = \left( 0.70588 \right) \times 100\% \approx 70\%$

Thus, the farmer needs to continue watering approximately 70% of the fields.

The correct answer, therefore, is choice 3: 70%.

To determine the percentage of the project that Dan has completed, we'll perform the following steps:

• Step 1: Recognize the total number of survey responses that Dan has received: 35 out of 49.
• Step 2: Apply the percentage formula: $\text{Percentage Completed} = \left(\frac{35}{49}\right) \times 100\%$.
• Step 3: Calculate the fraction: $\frac{35}{49} = 0.7142857$ (approximate).
• Step 4: Convert this decimal to a percentage: $0.7142857 \times 100 \approx 71.42857\%$.
• Step 5: Round the result if necessary to obtain a whole number percentage. In this case, $71.42857\%$ rounds to $71\%$.

Therefore, the approximate percentage of the project that Dan has completed is $\textbf{71\%}$.

To solve this problem, we'll follow these steps:

• Step 1: Determine the total number of apartments in the building.
• Step 2: Apply the percentage formula to find the percentage of occupied apartments.
• Step 3: Compare the calculated percentage with the choices provided.

Now, let's work through each step:

Step 1: Calculate the total number of apartments.
The building has 34 floors and each floor has 7 apartments, so the total number of apartments is:
$34 \times 7 = 238$

Step 2: Use the percentage formula to find the occupancy rate.
The total number of occupied apartments is 59. So, the percentage of occupied apartments is calculated as:
$\left(\frac{59}{238}\right) \times 100$

Performing the calculation, we get:
$\left(\frac{59}{238}\right) \times 100 \approx 24.79\%$

Rounding to the nearest whole number, this is approximately $25\%$.

Step 3: Compare with choices:
The correct answer, rounding to the nearest whole number, matches choice number 2: 25%.

Therefore, the solution to the problem is $25\%$.

To solve this problem, let's go through these steps:

• Step 1: Calculate the distance Ron has already covered. Given his speed of 9 km/h and time of 3 hours:
  $\text{Distance covered} = 9 \, \text{km/h} \times 3 \, \text{hours} = 27 \, \text{km}$
• Step 2: Find the remaining distance Ron needs to run:
  $\text{Remaining distance} = 39 \, \text{km} - 27 \, \text{km} = 12 \, \text{km}$
• Step 3: Calculate the percentage of the route remaining:
  $\text{Percentage remaining} = \left( \frac{12 \, \text{km}}{39 \, \text{km}} \right) \times 100 \approx 30.77\%$

Therefore, rounding to the nearest whole number, approximately 31% of Ron's running route remains.

To solve this problem, we'll follow these steps:

• Step 1: Calculate the total number of students in the school.
• Step 2: Calculate the percentage of students who are taller than Silvana.

Now, let's work through each step:
Step 1: Silvana's school has 5 classes, each with 32 students. To find the total number of students, we multiply the number of classes by the number of students per class:
$5 \times 32 = 160 \text{ students}$.

Step 2: We know 40 students are taller than Silvana. We use the percentage formula to find the percentage of students taller than Silvana:
$\frac{40}{160} \times 100\% = 25\%$.

Therefore, the answer to Silvana's question is 25%.