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A hot air balloon rose at a constant rate. After $3$ minutes, the balloon was $44$ meters above the ground. Then, $2$ minutes later, the hot air balloon had risen to $70$ meters above the ground. $\newline$ How much did the hot air balloon rise each minute? $\newline$ meters $\newline$ How far above the ground was the hot air balloon at the start of the ride? $\newline$ meters $\newline$ Complete the equation that describes the relationship between the altitude of the hot air balloon in meters, $A$ , and the elapsed time in minutes, $t$ . $\newline$ Write your answer using whole numbers or decimals rounded to the nearest tenth. $\newline$ A = t +

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Evaluate two-variable equations: word problems

Full solution

Q. A hot air balloon rose at a constant rate. After

3

minutes, the balloon was

44

meters above the ground. Then,

2

minutes later, the hot air balloon had risen to

70

meters above the ground.

\newline

How much did the hot air balloon rise each minute?

\newline

____ meters

\newline

How far above the ground was the hot air balloon at the start of the ride?

\newline

____ meters

\newline

Complete the equation that describes the relationship between the altitude of the hot air balloon in meters,

A

, and the elapsed time in minutes,

t

.

\newline

Write your answer using whole numbers or decimals rounded to the nearest tenth.

\newline

A = ____ t + ____

Calculate rate of ascent: Calculate the rate of ascent between the $3$ -minute and $5$ -minute marks. $\newline$ Difference in altitude: $70$ meters - $44$ meters = $26$ meters. $\newline$ Time difference: $5$ minutes - $3$ minutes = $2$ minutes. $\newline$ Rate of ascent: $\frac{26 \text{ meters}}{2 \text{ minutes}} = 13 \text{ meters per minute}$ .
Determine initial altitude: Determine the altitude of the hot air balloon at the start of the ride. $\newline$ Altitude at $3$ minutes: $44$ meters. $\newline$ Time from start to $3$ minutes: $3$ minutes. $\newline$ Initial altitude: $44$ meters - ( $13$ meters/minute $\times$ $3$ minutes) = $5$ meters.
Formulate equation: Formulate the equation relating altitude $A$ to time $t$ . Using the rate of ascent and the initial altitude: $A = 13t + 5$ .

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\newline

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