Math Snap

STEP 1

1. We need to determine the base number from which a given percentage results in a known value.
2. The problem involves basic percentage calculations and algebraic manipulations.
3. The final result should be a single number.

STEP 2

1. Formulate the equation for the first problem (50 is $20\%$ of what number?).
2. Solve the equation to find the unknown number.
3. Formulate the equation for the second problem ($24\%$ of what is 200?).
4. Solve the equation to find the unknown number.

STEP 3

Formulate the equation for the first problem. Let $x$ be the unknown number. According to the problem, $50$ is $20\%$ of $x$.
$$50 = 0.20x$$

STEP 4

Solve the equation for $x$ by isolating $x$ on one side of the equation.
$$x = \frac{50}{0.20}$$

STEP 5

Calculate the value of $x$.
$$x = 250$$

STEP 6

Formulate the equation for the second problem. Let $y$ be the unknown number. According to the problem, $24\%$ of $y$ is $200$.
$$0.24y = 200$$

STEP 7

Solve the equation for $y$ by isolating $y$ on one side of the equation.
$$y = \frac{200}{0.24}$$

Calculate the value of $y$.
$$y \approx 833.33$$ Solution:
For problem 23, the unknown number is $250$.
For problem 25, the unknown number is approximately $833.33$.