Math Snap

STEP 1

1. The initial altitude of the hot air balloon is $100 \frac{1}{5}$ yards.
2. The balloon's altitude decreases by $10 \frac{4}{5}$ yards every minute.
3. We need to determine the number of minutes, $m$, it will take for the balloon to reach an altitude of 57 yards.
4. We are given four potential equations to choose from.

STEP 2

1. Understand the problem and the relationship between the variables.
2. Translate the problem into a mathematical equation.
3. Identify the correct equation from the given options.

STEP 3

Understand the problem and the relationship between the variables.
The balloon starts at $100 \frac{1}{5}$ yards and decreases its altitude by $10 \frac{4}{5}$ yards per minute. We want to find out how many minutes, $m$, it will take for the balloon to reach 57 yards.

STEP 4

Translate the problem into a mathematical equation.
The altitude of the balloon after $m$ minutes can be expressed as:
$$\text{Initial altitude} - (\text{Rate of decrease} \times m) = \text{Final altitude}$$ Substituting the given values:
$$100 \frac{1}{5} - 10 \frac{4}{5} \times m = 57$$

Identify the correct equation from the given options.
The equation we derived is:
$$100 \frac{1}{5} - 10 \frac{4}{5} \times m = 57$$ This matches option D.
The correct equation is:
$$\boxed{D) \, 100 \frac{1}{5} - 10 \frac{4}{5} m = 57}$$