Question
V
2
A hardware store charges a $30 rental fee and $15 per day to rent a power washer. Which equation correctly relates the total cost y to rent the washer for x days?
A y = 15 + 30x
C y = 30 - 15
B
y = 30 + 15x
D y = 15 -
30
Tony drives 18 miles to pick up his friend at his house.
Then he drives at a constant speed of 40 miles per hour to a state park to go hiking. Let y represent the number of miles that Tony drives after x hours. Which of the following statements are true? Select all that apply.
The relationship can be represented by the
equation y = 40x + 18.
B If Tony travels for 1.5 hours, he will have driven a
total of 60 miles.
The initial value is 18 miles.
D
The rate of change is negative.
What do the parts f each equatior represent?
How do you determine the initial value and rate of change?
3
Alma borrows money from her mom to buy a $150 bike.
She gives her mom $40 at the time of purchase and continues to pay her $10 each month until the bike is paid for in full. Alma wrote this equation to represent the amount y that she will have paid her mom after x months.
Equation: y = 40x + 10
Is her equation correct? How did she get that equation?
If it is not correct, write a correct equation.
2
A hardware store charges a $30 rental fee and $15 per day to rent a power washer. Which equation correctly relates the total cost y to rent the washer for x days?
A y = 15 + 30x
C y = 30 - 15
B
y = 30 + 15x
D y = 15 -
30
Tony drives 18 miles to pick up his friend at his house.
Then he drives at a constant speed of 40 miles per hour to a state park to go hiking. Let y represent the number of miles that Tony drives after x hours. Which of the following statements are true? Select all that apply.
The relationship can be represented by the
equation y = 40x + 18.
B If Tony travels for 1.5 hours, he will have driven a
total of 60 miles.
The initial value is 18 miles.
D
The rate of change is negative.
What do the parts f each equatior represent?
How do you determine the initial value and rate of change?
3
Alma borrows money from her mom to buy a $150 bike.
She gives her mom $40 at the time of purchase and continues to pay her $10 each month until the bike is paid for in full. Alma wrote this equation to represent the amount y that she will have paid her mom after x months.
Equation: y = 40x + 10
Is her equation correct? How did she get that equation?
If it is not correct, write a correct equation.
Answers
GPT-4o mini
Let's break down each problem and address them step by step.
### Problem 1: Power Washer Rental Cost
**Given Information:**
- Fixed rental fee: $30
- Daily rental charge: $15 per day
- Let \( y \) be the total cost.
- Let \( x \) be the number of days rented.
**Equation Creation:**
The total cost can be expressed as a sum of the fixed fee and the total daily charges. So the correct equation relating \( y \) to \( x \) would be:
\[
y = 30 + 15x
\]
This represents the $30 fixed cost plus the $15 multiplied by the number of days rented.
**Correct Answer:** B \( y = 30 + 15x \)
---
### Problem 2: Tony's Driving Distance
**Given Information:**
- Tony drives 18 miles initially.
- He drives at a speed of 40 miles per hour.
Let \( y \) represent the distance traveled after \( x \) hours. The correct representation of this relationship is:
\[
y = 40x + 18
\]
**Statement Evaluation:**
1. **True:** The relationship can be represented by the equation \( y = 40x + 18 \).
2. **True:** If \( x = 1.5 \) hours, then:
\[
y = 40(1.5) + 18 = 60 + 18 = 78 \text{ miles}
\]
*Note: There seems to be an error with the statement indicating 60 miles instead of 78 miles.*
3. **True:** The initial value is 18 miles (the distance before starting to drive).
4. **False:** The rate of change is not negative. It's positive since he is driving away from his starting point.
**Correct Statements:** 1 (True), 3 (True)
---
### Problem 3: Alma's Bike Payment Equation
**Given Information:**
- Total price of the bike: $150
- Initial payment: $40
- Monthly payments: $10
**Understanding Payments:**
- After paying $40 at purchase, Alma owes \( 150 - 40 = 110 \) dollars.
- From that point, she pays \( 10 \) dollars per month.
So, the total amount \( y \) paid after \( x \) months can be written as:
\[
y = 40 + 10x
\]
Alma's original equation \( y = 40x + 10 \) is incorrect because the initial payment should not be multiplied by \( x \). Instead, the initial payment should be a constant added to the series of monthly payments.
**Correct Equation:**
\[
y = 40 + 10x
\]
This shows the $40 paid initially and an additional $10 for each month she is making payments.
### Problem 1: Power Washer Rental Cost
**Given Information:**
- Fixed rental fee: $30
- Daily rental charge: $15 per day
- Let \( y \) be the total cost.
- Let \( x \) be the number of days rented.
**Equation Creation:**
The total cost can be expressed as a sum of the fixed fee and the total daily charges. So the correct equation relating \( y \) to \( x \) would be:
\[
y = 30 + 15x
\]
This represents the $30 fixed cost plus the $15 multiplied by the number of days rented.
**Correct Answer:** B \( y = 30 + 15x \)
---
### Problem 2: Tony's Driving Distance
**Given Information:**
- Tony drives 18 miles initially.
- He drives at a speed of 40 miles per hour.
Let \( y \) represent the distance traveled after \( x \) hours. The correct representation of this relationship is:
\[
y = 40x + 18
\]
**Statement Evaluation:**
1. **True:** The relationship can be represented by the equation \( y = 40x + 18 \).
2. **True:** If \( x = 1.5 \) hours, then:
\[
y = 40(1.5) + 18 = 60 + 18 = 78 \text{ miles}
\]
*Note: There seems to be an error with the statement indicating 60 miles instead of 78 miles.*
3. **True:** The initial value is 18 miles (the distance before starting to drive).
4. **False:** The rate of change is not negative. It's positive since he is driving away from his starting point.
**Correct Statements:** 1 (True), 3 (True)
---
### Problem 3: Alma's Bike Payment Equation
**Given Information:**
- Total price of the bike: $150
- Initial payment: $40
- Monthly payments: $10
**Understanding Payments:**
- After paying $40 at purchase, Alma owes \( 150 - 40 = 110 \) dollars.
- From that point, she pays \( 10 \) dollars per month.
So, the total amount \( y \) paid after \( x \) months can be written as:
\[
y = 40 + 10x
\]
Alma's original equation \( y = 40x + 10 \) is incorrect because the initial payment should not be multiplied by \( x \). Instead, the initial payment should be a constant added to the series of monthly payments.
**Correct Equation:**
\[
y = 40 + 10x
\]
This shows the $40 paid initially and an additional $10 for each month she is making payments.