Quantity, percentage, percentage value: Change in two elements

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

• Step 1: Identify the given information.
• Step 2: Use the appropriate formula to determine the total capacity of the pool.
• Step 3: Perform the necessary calculations to find the answer.

Now, let's work through each step:

Step 1: We are informed that 40% of the pool's capacity is filled with 180 $m^3$ of water.
This means that 40% of the pool's total capacity equals 180 $m^3$.

Step 2: To find the total capacity (denoted by $T$), use the percentage formula:
$T = \frac{\text{Percentage value}}{\left( \frac{\text{Percentage}}{100} \right)}$

Step 3: Substitute the known values into the formula:
$T = \frac{180}{\left( \frac{40}{100} \right)}$

This simplifies to:
$T = \frac{180}{0.4} = 450$

Therefore, the total capacity of the pool is 450 $m^3$.

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

• Step 1: Determine how much the first person receives by calculating 40% of $7000.
• Step 2: Determine how much the second person receives by calculating 15% of $7000.
• Step 3: Calculate the amount the third person receives by finding the remainder after the first two allocations.

Let's proceed with each step:
Step 1: Calculate 40% of $7000. The formula to use is:

Thus, the first person receives $2800.

Step 2: Calculate 15% of $7000. Using the same formula:

Therefore, the second person receives $1050.

Step 3: Calculate the remaining amount for the third person:

This means the third person receives $3150.

To confirm, the total $7000 is distributed correctly as $2800 + 1050 + 3150 = 7000$.

Thus, the amount received by each person is:

• The first person received $2800.
• The second person received $1050.
• The third person received $3150.

Therefore, the correct solution is choice #3.

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

• Step 1: Determine the total number of students in the class.
• Step 2: Calculate how many students attend the dance class.

Now, let's work through each step:
Step 1: We know that 6 students are 24% of the class. We use the formula for determining the whole number from a percentage:

So, the total number of 9th grade students is 25.

Step 2: Now that we have the total number of students, we can find how many attend the dance class (16% of 25):

Thus, the number of students attending the dance class is 4 students.

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

• Step 1: Calculate the number of eighth-grade students
• Step 2: Calculate the number of seventh-grade students
• Step 3: Sum the number of students from the seventh and eighth grades

Now, let's work through each step:
Step 1: The eighth-grade students make up 25% of the students. Therefore, the number of eighth-grade students is $180 \times \frac{25}{100} = 45$ students.

Step 2: The seventh-grade students make up 40% of the students. Therefore, the number of seventh-grade students is $180 \times \frac{40}{100} = 72$ students.

Step 3: Adding the number of students from the seventh and eighth grades gives us: $45 + 72 = 117$ students.

Therefore, the number of students from the seventh and eighth grades that go on the trip is 117 students.

To solve this problem, we will walk through each step sequentially:

• Step 1: Calculate the price after a 10% increase.

• Step 2: Calculate the price after a 15% decrease from the increased price.

Now, let's work through these steps:
Step 1: The original price of the air conditioner is $\$2500$. When the price is increased by 10%, the new price is calculated as follows: $\text{New price after 10\% increase} = 2500 \times \left(1 + \frac{10}{100}\right) = 2500 \times 1.10 = 2750$

Step 2: This increased price of \$2750 is then decreased by 15%. The new price after this decrease is calculated by:

$\text{Final price after 15\% decrease} = 2750 \times \left(1 - \frac{15}{100}\right) = 2750 \times 0.85 = 2337.5$

Therefore, the price of the air conditioner at the end of the season is $2337.5$ dollars.