Question
Michael is driving on a long road trip. He wrote an equation to represent how many gallons of gas he has left in his tank, \( g=8-0.5 h \), where \( g \) represents the number of gallons and \( h \) represents time in hours. What could the number 8 represent in the equation?
Ask by Grant O'Quinn. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The number 8 represents the initial amount of gas in gallons that Michael had in his tank at the start of his trip.
Solution
In the equation \( g = 8 - 0.5h \), the variable \( g \) represents the number of gallons of gas left in Michael's tank, and \( h \) represents the time in hours that he has been driving.
The number 8 in this equation represents the initial amount of gas in gallons that Michael had in his tank at the start of his trip (when \( h = 0 \)). This means that when he starts driving (at \( h = 0 \)), he has 8 gallons of gas. As time progresses and he drives, the amount of gas decreases by 0.5 gallons for each hour he drives, which is represented by the term \( -0.5h \).
Thus, the number 8 indicates the starting quantity of gas in the tank.
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Simplify this solution Bonus Knowledge
In the equation \( g=8-0.5 h \), the number 8 represents the total amount of gas in gallons that Michael started with in his tank before he began his road trip. It’s like the “gas tank full” status, giving him a solid starting point for his calculations! Additionally, when considering the equation in a real-world application, Michael can easily calculate how long he can drive before needing to refuel. For instance, if he knows that he consumes 0.5 gallons per hour, he can determine how long the 8 gallons will last by setting \( g \) to 0 and solving for \( h \). This could help him plan his stops along the way!
