Quantity, percentage, percentage value: Finding the whole using a part

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

• Step 1: Identify the given information.
• Step 2: Apply the appropriate formula for finding the whole.
• Step 3: Perform the necessary calculations.

Now, let's work through each step:
Step 1: We are given that 15 percent of some whole amount is equal to 3.
Step 2: We use the formula for calculating the whole:

Substituting the given values into the formula:
The part is 3, and the percentage is 15%. Thus, we calculate:

Step 3: Simplify the expression:
First, convert 15% to a decimal by dividing by 100, which gives 0.15.
Now calculate:

Perform the division:

Therefore, the solution to the problem is $20$.

To solve this problem, we need to find the whole value when 27% of it equals 4. We'll use the percentage formula:

$\text{Percentage} = \left(\frac{\text{Part}}{\text{Whole}}\right) \times 100$

We know the percentage is 27%, and the part is 4. Substituting these values, we have:

$27 = \left(\frac{4}{\text{Whole}}\right) \times 100$

To find the whole, rearrange the equation:

$27 = \frac{4}{\text{Whole}} \times 100$

Now, solve for the whole:

$\text{Whole} = \frac{4 \times 100}{27}$

$\text{Whole} = \frac{400}{27}$

By calculating the division:

$\text{Whole} \approx 14.81$

Therefore, the solution to the problem is $14.81$.

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

• Step 1: Convert the given percentage to a decimal.
• Step 2: Use the formula to solve for the whole.
• Step 3: Calculate and identify the correct option.

Now, let's work through each step:
Step 1: The given percentage is 64%. To convert it to a decimal, we divide by 100: $64\% = 0.64$.

Step 2: Use the formula for finding the whole:
$\text{Whole} = \frac{\text{Part}}{\text{Percentage as a decimal}} = \frac{5}{0.64}$

Step 3: Perform the division:
$\frac{5}{0.64} = 7.8125$

Therefore, rounding to two decimal places, the whole is $7.81$.

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

• Step 1: Convert the given percentage to a decimal by dividing by 100.

• Step 2: Use the formula to find the whole number based on the part and the percentage in decimal form.

• Step 3: Verify that the calculated whole corresponds to the multiple choice answers provided.

Now, let's work through each step:
Step 1: Convert 40% to decimal form. This gives us $0.40$.
Step 2: Use the formula for the whole:
$\text{Whole} = \frac{\text{Part}}{\text{Percentage in decimal}} = \frac{2}{0.40}$ Calculate this division: $\frac{2}{0.40} = 5$
Step 3: Verify: The whole number calculated is 5, a valid option in the multiple-choice answers.
Therefore, the solution to the problem is $5$.

To solve this problem, we'll proceed with the following steps:

• Step 1: Identify the given information.
• Step 2: Apply the appropriate formula for the percentage calculation.
• Step 3: Perform the necessary calculations to find the whole number.

Now, let's work through each step:

Step 1: The problem states that 60% of a number is equal to 4. We need to find this number, denoted as the whole.

Step 2: We'll use the percentage formula: $\text{whole} = \frac{\text{part} \times 100}{\text{percentage}}$

Step 3: Plugging in the values, we have: $\text{whole} = \frac{4 \times 100}{60}$ $\text{whole} = \frac{400}{60}$ $\text{whole} = \frac{20}{3}$

Simplifying further, $\text{whole} \approx 6.66$

Therefore, the solution to the problem is $6.66$.

To solve this problem, we'll calculate the whole number using the provided percentage and part of that percentage.

• Step 1: The given part is 7, which corresponds to 35% of the whole.
• Step 2: Use the formula: $\text{whole} = \frac{\text{part} \times 100}{\text{percentage}}$
• Step 3: Substitute the known values: $\text{whole} = \frac{7 \times 100}{35}$
• Step 4: Calculate $7 \times 100 = 700$.
• Step 5: Divide by 35: $\text{whole} = \frac{700}{35}$
• Step 6: Simplify the division: $\text{whole} = 20$

Therefore, the whole number when 35% is equal to 7 is 20.

To solve this problem, we will find a common equation to account for all students:

• Activity: Playing catch, Fraction: $\frac{1}{5}x$
• Activity: Playing soccer, Fraction: 20% of $x$ which is $\frac{1}{5}x$
• Activity: Watching a movie, Number: $15$ students

The total number of students involved is $x$. Thus, the setup for the equation is:

$\frac{1}{5}x + \frac{1}{5}x + 15 = x$

Simplify and solve for $x$:

$\frac{2}{5}x + 15 = x$

Subtract $\frac{2}{5}x$ from both sides:

$15 = x - \frac{2}{5}x$

$15 = \frac{3}{5}x$

To isolate $x$, multiply both sides by $\frac{5}{3}$:

$x = 15 \times \frac{5}{3}$

$x = 25$

Therefore, the total number of students is 25 students.

To solve this problem, follow these steps:

• Step 1: Define the total number of dolls in the toy shop as $x$.
• Step 2: Note that 30% of these dolls are standard issue, thus $0.30x$ are standard issue dolls.
• Step 3: Since 70% of the dolls are limited edition (as standard and limited edition must account for 100% of the shop's dolls), $0.70x$ would be limited edition dolls.
• Step 4: Set up the equation: $0.70x = 21$, since we know the exact count of limited edition dolls is 21.
• Step 5: Solve for $x$ by dividing both sides of the equation by 0.70:

Therefore, the total number of dolls in the shop is $30$.