Answer :
Let's solve each part of the problem step-by-step.
1. Which expression describes the gallons of gas in the tank after [tex]\(d\)[/tex] days?
We need to choose the expression that represents the amount of gas left in the tank after [tex]\(d\)[/tex] days.
Considering the options:
- [tex]\(14 - 0.5d\)[/tex] means you start with 14 gallons and lose 0.5 gallons every day. This fits a common situation where gas is consumed daily.
- Checking the logical options, this seems the most probable choice because the starting amount is reduced by a daily consumption.
Therefore, the correct expression is:
A. [tex]\(14 - 0.5d\)[/tex]
---
2. Renting a ski boat problem
You want to spend no more than [tex]$125. The cost to rent a ski boat is $[/tex]20 plus [tex]$35 per hour. We need to determine how many hours you can rent the boat.
Let's break it down into an inequality:
- Start cost: \(\$[/tex]20\)
- Hourly cost: [tex]\(\$35\)[/tex]
- Maximum budget: [tex]\(\$125\)[/tex]
The inequality representing this situation is:
[tex]\[ 20 + 35h \leq 125 \][/tex]
Steps to solve the inequality:
1. Subtract the fixed cost from the maximum budget:
[tex]\[ 125 - 20 = 105 \][/tex]
2. Divide the remaining amount by the hourly cost to find out how many full hours you can afford:
[tex]\[105 \div 35 = 3\][/tex]
Therefore, you can rent the ski boat for a maximum of 3 hours without exceeding the budget of $125.
1. Which expression describes the gallons of gas in the tank after [tex]\(d\)[/tex] days?
We need to choose the expression that represents the amount of gas left in the tank after [tex]\(d\)[/tex] days.
Considering the options:
- [tex]\(14 - 0.5d\)[/tex] means you start with 14 gallons and lose 0.5 gallons every day. This fits a common situation where gas is consumed daily.
- Checking the logical options, this seems the most probable choice because the starting amount is reduced by a daily consumption.
Therefore, the correct expression is:
A. [tex]\(14 - 0.5d\)[/tex]
---
2. Renting a ski boat problem
You want to spend no more than [tex]$125. The cost to rent a ski boat is $[/tex]20 plus [tex]$35 per hour. We need to determine how many hours you can rent the boat.
Let's break it down into an inequality:
- Start cost: \(\$[/tex]20\)
- Hourly cost: [tex]\(\$35\)[/tex]
- Maximum budget: [tex]\(\$125\)[/tex]
The inequality representing this situation is:
[tex]\[ 20 + 35h \leq 125 \][/tex]
Steps to solve the inequality:
1. Subtract the fixed cost from the maximum budget:
[tex]\[ 125 - 20 = 105 \][/tex]
2. Divide the remaining amount by the hourly cost to find out how many full hours you can afford:
[tex]\[105 \div 35 = 3\][/tex]
Therefore, you can rent the ski boat for a maximum of 3 hours without exceeding the budget of $125.
