Quantity, percentage, percentage value: Worded problems

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, 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, 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 find the number of female students in the seventh grade, we first identify the number of male students and then subtract that from the total number of students.

Step 1: Calculate the number of male students.
Percentage of male students = 40% = 0.40
Total number of students = 180
Number of male students = 180 × 0.40
Number of male students = $72$

Step 2: Calculate the number of female students.
Total number of students = 180
Number of female students = Total number of students - Number of male students
Number of female students = 180 - 72
Number of female students = $108$