Quantity, percentage, percentage value: Change in two elements

Applying the formulaCalculate the percentage of the whole numberCalculation using percentagesConvert fractions to percentagesExpress one number as a percentage of anotherFinding the whole using a partPricing strategies including discounts and markupsThe Whole number is 100The Whole number is a Multiple of 100The Whole number is Greater than 100Two changes in percentagesWorded problems
Question 1

A pool was filled with water over the course of two days:

If on the first day, the pool was filled with 180 \( m^3 \) of water constituting 40%.

What is the total amount of water used to fill the pool?

Question 2

7000 $ was shared between three people.

The first person received 40% of the total, the second person received 15% of the total and the third person received the remainder.

How much money did they each receive?

Question 3

Six 9th grade students attend acting classes. They make up 24 percent of the class as a whole.

A further 16% of the 9th grade students attend dance class.

The rest of the students do not participate in any extracurricular classes.

How many students attend the dance class?

Question 4

A group of students and teachers go on a school trip, of which 180 are students.
25% of the group are from the eighth grade, 20% are from the ninth grade, 40% are from the seventh grade, and the rest of the group are teachers.

How many students from the seventh and eighth grades go on the trip?

Examples with solutions for Quantity, percentage, percentage value: Change in two elements

Exercise #1

A pool was filled with water over the course of two days:

If on the first day, the pool was filled with 180 m3 m^3 of water constituting 40%.

What is the total amount of water used to fill the pool?

Video Solution

Step-by-Step Solution

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 m3 m^3 of water.
This means that 40% of the pool's total capacity equals 180 m3 m^3 .

Step 2: To find the total capacity (denoted by T T ), use the percentage formula:
T=Percentage value(Percentage100) T = \frac{\text{Percentage value}}{\left( \frac{\text{Percentage}}{100} \right)}

Step 3: Substitute the known values into the formula:
T=180(40100) T = \frac{180}{\left( \frac{40}{100} \right)}

This simplifies to:
T=1800.4=450 T = \frac{180}{0.4} = 450

Therefore, the total capacity of the pool is 450 m3 m^3 .

Answer

450 m³

Exercise #2

7000 $ was shared between three people.

The first person received 40% of the total, the second person received 15% of the total and the third person received the remainder.

How much money did they each receive?

Video Solution

Step-by-Step Solution

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

  • Step 1: Determine how much the first person receives by calculating 40% of 7000.</li><li>Step2:Determinehowmuchthesecondpersonreceivesbycalculating157000.</li> <li>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:

\( \text{Amount} = \frac{40}{100} \times 7000 = 2800

Thus, the first person receives 2800</strong>.</p><p><strong>Step2:</strong>Calculate152800</strong>.</p> <p><strong>Step 2:</strong> Calculate 15% of 7000. Using the same formula:

Amount=15100×7000=1050 \text{Amount} = \frac{15}{100} \times 7000 = 1050

Therefore, the second person receives 1050.

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

\( \text{Remainder} = 7000 - (2800 + 1050) = 3150

This means the third person receives 3150</strong>.</p><p>Toconfirm,thetotal3150</strong>.</p> <p>To confirm, the total 7000 is distributed correctly as 2800+1050+3150=70002800 + 1050 + 3150 = 7000.

Thus, the amount received by each person is:

  • The first person received 2800.</li><li>Thesecondpersonreceived2800.</li> <li>The second person received 1050.
  • The third person received $3150.

Therefore, the correct solution is choice #3.

Answer

The first person received 2800 dollars: the second person received 1050 dollars and the third person received 3150 dollars.

Exercise #3

Six 9th grade students attend acting classes. They make up 24 percent of the class as a whole.

A further 16% of the 9th grade students attend dance class.

The rest of the students do not participate in any extracurricular classes.

How many students attend the dance class?

Video Solution

Step-by-Step Solution

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:

Total number of students=Number of students attending actingPercentage×100=60.24=25 \text{Total number of students} = \frac{\text{Number of students attending acting}}{\text{Percentage}} \times 100 = \frac{6}{0.24} = 25

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):

Number of students in dance classes=0.16×25=4 \text{Number of students in dance classes} = 0.16 \times 25 = 4

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

Answer

4 students

Exercise #4

A group of students and teachers go on a school trip, of which 180 are students.
25% of the group are from the eighth grade, 20% are from the ninth grade, 40% are from the seventh grade, and the rest of the group are teachers.

How many students from the seventh and eighth grades go on the trip?

Video Solution

Step-by-Step Solution

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 180×25100=45 180 \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 180×40100=72 180 \times \frac{40}{100} = 72 students.

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

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

Answer

117 students