Quantity, percentage, percentage value: Worded problems

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

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

Now, let's work through each step:

Step 1: The total weight of the cake is $2\, \text{kg}$, and chocolate makes up $10\%$ of this.

Step 2: To find the weight of the chocolate, we use the formula: $\text{Chocolate weight} = \left( \frac{\text{Percentage}}{100} \right) \times \text{Total weight of the cake}$ This is: $\text{Chocolate weight} = \left( \frac{10}{100} \right) \times 2$

Step 3: Performing the calculation: $= 0.1 \times 2 = 0.2$

Therefore, the weight of the chocolate in the cake is $0.2\, \text{kg}$.

Checking the multiple-choice options, the correct choice is the one with $0.2$, which corresponds to choice $4$.

To solve this problem, we will determine the number of white balls in the box using a fraction of the total number of balls.

We are given the total number of balls in the box as 18, and we know that $\frac{2}{3}$ of these balls are white. To find the number of white balls, we follow these steps:

• Step 1: Identify the total quantity, which is 18 balls.
• Step 2: Use the given fraction $\frac{2}{3}$ to find the number of white balls.
• Step 3: Multiply the total number of balls by the fraction of white balls: $18 \times \frac{2}{3}$.

Perform the calculation:

$18 \times \frac{2}{3} = 18 \times 0.6667 = 12$

Alternatively, calculate directly using fractions:

$18 \times \frac{2}{3} = \frac{18 \times 2}{3} = \frac{36}{3} = 12$

Thus, the total number of white balls in the box is 12.

Therefore, the correct answer is choice 12.

To solve this problem, we'll determine the number of orange balls by calculating the fraction of the total number of balls:

• Step 1: Identify the total number of balls, $28$.
• Step 2: Note the fraction representing the orange balls, $\frac{1}{4}$.
• Step 3: Apply the formula to find the number of orange balls:
  Number of orange balls $= 28 \times \frac{1}{4}$

Now, let's perform the calculation:
$28 \times \frac{1}{4} = 28 \div 4 = 7$

Therefore, the number of orange balls in the box is $7$.

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

• Step 1: Calculate the weight of water.
• Step 2: Convert this weight into volume (cubic centimeters).

Let's work through each step:

Step 1: Calculate the weight of water.
The total weight of the jar's contents is 500 grams. Since 25% of this weight is water, we calculate the weight of water as follows:

$\text{Weight of water} = 25\% \times 500 \text{ grams}$

$\text{Weight of water} = 0.25 \times 500 = 125 \text{ grams}$

Step 2: Convert the weight into volume.
Given that the density of water is 1 gram per cubic centimeter, the volume of water can be directly found as follows:

$\text{Volume of water (in cm}^3\text{)} = \text{Weight of water (in grams)}$

$\text{Volume of water} = 125 \text{ cm}^3$

Therefore, the solution to the problem is 125 cubic centimeters of water.

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

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

Let's go through each step:
Step 1: The original price of the coat is $200, and the discount percentage is 20%.

Step 2: We use the formula to calculate the discount amount:
$\text{Discount Amount} = \text{Original Price} \times \left(\frac{\text{Discount Percentage}}{100}\right)$

Step 3: Substitute the given values into the formula:
$\text{Discount Amount} = 200 \times \left(\frac{20}{100}\right) = 200 \times 0.2 = 40$

Therefore, the price of the coat decreases by $\$40$ after the discount.

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

• Step 1: Identify the given information.
• Step 2: Apply the appropriate percentage calculation.
• Step 3: Perform the mathematical operations.

Now, let's work through each step:

Step 1: The total number of children in the class is 32, and 50% of these children are boys.

Step 2: We need to find 50% of 32. This can be calculated by using the formula for percentage:

$\text{Number of boys} = \left(\frac{50}{100}\right) \times 32$

Step 3: Simplify the calculation:

$\frac{50}{100} = 0.5$

Thus, the calculation becomes:

$0.5 \times 32 = 16$

Therefore, the solution to the problem is that there are 16 boys in the class.

In order to answer the question we must first understand how much the ticket costs:

45-40=5

That is, the price of the ticket increased by 5$.

Now we need to determine what the percentage value of the 5 pesos increase is. In order to determine this we will divide the increase by the original price and multiply it by 100 to convert it into a percentage.

5/40 * 100

We start by converting the 100 into fraction form.

5/40 * 100/1

When there is a multiplication of fractions, we can multiply numerator by numerator and denominator by denominator.

5*100 / 40*1

500 / 40

Thus we simplify as follows:

50/4

Lastly we convert the fraction into its complete form.

50/4 = 12.5

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

• Step 1: Identify the percentage of the initial amount needed.
• Step 2: Calculate the corresponding amount of water using the percentage formula.

Now, let's work through each step:

Step 1: We need to find 35% of the initial 1000 liters.

Step 2: Using the formula to find a percentage of a number, we have:

Calculating this gives:

= 350

Therefore, the number of liters left in the pool after three days is $350$ liters.

To solve the problem, we will calculate the amount that William will receive by following these steps:

• Step 1: Convert the percentage to a decimal by dividing by 100. Since William's portion is 20%, convert it to decimal: $0.20$.

• Step 2: Multiply the total amount by this decimal to find William's share: $0.20 \times 3000$.

Now, carrying out the multiplication:
$0.20 \times 3000 = 600$
Thus, William will receive $\$600$.

Therefore, the solution to the problem is $600$, which corresponds to choice 3 in the options provided.

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

• Step 1: Identify the total number of people, which is 140.
• Step 2: Recognize that 60% of these are adults.
• Step 3: Convert 60% into a decimal fraction: $\frac{60}{100} = 0.6$.
• Step 4: Multiply the total number of people by the decimal fraction: $0.6 \times 140$.

Now, let's perform the calculation:
Step 1: We have 140 people in total.
Step 2: 60% of these are adults.
Step 3: Converting 60% to a decimal gives us 0.6.
Step 4: Multiply 0.6 by 140:

$0.6 \times 140 = 84$

Therefore, the number of adults in the group is 84.

$40-8=32$

In order to determine percentages, we must make use of the two pieces of information in our possession: the total amount ($40) and the discount (20%).

This information can be inserted into the following formula:

$\frac{Price\times\text{Percentage}}{100}$

Which allows us to find the percentage of something.

We insert the given information:

$40\times\frac{20}{100}=$

$\frac{800}{100}=$

$8$

We then discover that the value of the discount is $8.

But we are not finished yet!

We need to subtract the discount from the original amount in order to determine the sale price:
$40-8=32$

To solve this problem, follow these steps:

• Identify original fuel quantity and calculate daily usage based on percentage.

• Determine the remaining fuel after the first day's usage.

• Calculate the liters used on the second day based on remaining fuel.

Let's go through the solution step-by-step:
Step 1: Calculate 10% of 60 liters (fuel used on the first day).
$\text{Fuel used on first day} = \frac{10}{100} \times 60 = 6 \text{ liters}$

Step 2: Calculate remaining fuel after the first day:
$\text{Remaining fuel} = 60 - 6 = 54 \text{ liters}$

Step 3: Calculate 15% of the remaining fuel for usage on the second day:
$\text{Fuel used on second day} = \frac{15}{100} \times 54 = 8.1 \text{ liters}$

Therefore, the amount of fuel used on the second day is 8.1 liters.

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 $30$.

To solve this problem, let's follow these steps:

• Step 1: Define the variables. Assume the price of a chair is $C$ dollars.

• Step 2: Determine the price increase for the table. Since the table's price is 150% greater than the chair's, calculate 150% of $C$, given by $1.5 \times C$.

• Step 3: Compute the table's price. The price $T$ of the table is the sum of the chair's price and the calculated increase: $T = C + 1.5 \times C$.

• Step 4: Simplify the expression. This results in $T = 2.5 \times C$.

Now, substituting values from the given options (since $T = 2.5 \times C$) reveals the following key information:

For option 3, with Chair at $100\$$, assuming Chair's price to be $C = 100$:
$T = 2.5 \times 100 = 250$.

Verification shows a chair price of $100\$$ and table price of $250\$$ as per our calculations. This matches our established equation, confirming it as the correct choice where a chair costs $100\$$ and a table costs $250\$$.

Thus, the individual prices are $C = 100 \ \text{dollars and} \ T = 250 \ \text{dollars}$, which aligns with option 3 in given choices.

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.

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: 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'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 tables manufactured in Holland using the given percentage.
• Step 2: Subtract that number from the total number of tables to find how many were manufactured in China.

Now, let's work through each step:
Step 1: The problem states that 25% of the tables were manufactured in Holland. We can calculate this quantity as follows:
$\text{Tables in Holland} = \frac{25}{100} \times 124 = 31$

Step 2: To find the number of tables manufactured in China, we subtract the number of tables manufactured in Holland from the total:

$\text{Tables in China} = 124 - 31 = 93$

Therefore, the number of tables manufactured in China is $93$.