Solving an Equation by Multiplication/ Division: Worded problems

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:

\begin{align*} 0.70x &= 21 \\ x &= \frac{21}{0.70} \\ x &= 30 \end{align*}

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.