Quantity, percentage, percentage value: Change in two elements

The Whole number is Greater than 100Two changes in percentagesApplying the formulaWorded problemsFinding the whole using a partPricing strategies including discounts and markupsCalculation using percentagesConvert fractions to percentagesThe Whole number is a Multiple of 100The Whole number is 100Express one number as a percentage of anotherCalculate the percentage of the whole number
Question 1

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?

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 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?

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

Exercise #1

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

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 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