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Math  /  Algebra

QuestionPart A A hot air balloon is at an altitude of 10015100 \frac{1}{5} yards. The balloon's altitude decreases by 104510 \frac{4}{5} yards every minute.
Which equation can be used to determine the number of minutes, mm, it will take the balloon to reach an altitude of 57 yards? A) 1045+10015m=5710 \frac{4}{5}+100 \frac{1}{5} m=57 B) 1045−10015m=5710 \frac{4}{5}-100 \frac{1}{5} m=57 C) 10015+1045m=57100 \frac{1}{5}+10 \frac{4}{5} m=57 D) 10015−1045m=57100 \frac{1}{5}-10 \frac{4}{5} m=57

Studdy Solution

STEP 1

1. The initial altitude of the hot air balloon is 10015 100 \frac{1}{5} yards.
2. The balloon's altitude decreases by 1045 10 \frac{4}{5} yards every minute.
3. We need to determine the number of minutes, m 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 10015 100 \frac{1}{5} yards and decreases its altitude by 1045 10 \frac{4}{5} yards per minute. We want to find out how many minutes, m 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 m minutes can be expressed as:
Initial altitude−(Rate of decrease×m)=Final altitude \text{Initial altitude} - (\text{Rate of decrease} \times m) = \text{Final altitude}
Substituting the given values:
10015−1045×m=57 100 \frac{1}{5} - 10 \frac{4}{5} \times m = 57

STEP 5

Identify the correct equation from the given options.
The equation we derived is:
10015−1045×m=57 100 \frac{1}{5} - 10 \frac{4}{5} \times m = 57
This matches option D.
The correct equation is:
D) 10015−1045m=57 \boxed{D) \, 100 \frac{1}{5} - 10 \frac{4}{5} m = 57}

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