Question
use proportional relationships to solve the following problem riley needs to earn enough money to purchas a new jacket
Answers
Answered by
GPT-4o mini
To solve the problem of how Riley can earn enough money to purchase a new jacket using proportional relationships, we will need a bit more information. Since the question is somewhat open-ended, we'll outline the steps and some examples.
1. **Determine the Cost of the Jacket**: Let's say the jacket costs \( P \) dollars.
2. **Find Out How Much Riley Can Earn**: We need to know how much money Riley earns per hour or per task. For instance, if Riley earns \( E \) dollars per hour, that means Riley can earn in a proportional relationship based on the time worked.
3. **Set Up the Proportional Relationship**:
- If \( H \) is the number of hours Riley can work, the total earnings can be expressed as:
\[
\text{Total Earnings} = E \times H
\]
- To ensure Riley can buy the jacket, set up the inequality:
\[
E \times H \geq P
\]
4. **Solve for Hours Needed**:
Rearranging the inequality gives:
\[
H \geq \frac{P}{E}
\]
This formula shows how many hours Riley needs to work to afford the jacket.
### Example:
Assume:
- The jacket costs \( P = 80 \) dollars.
- Riley earns \( E = 10 \) dollars per hour.
Using the formula:
\[
H \geq \frac{80}{10} = 8
\]
So, Riley needs to work at least 8 hours to earn enough money to purchase the jacket.
If you have specific numbers for the cost of the jacket and how much Riley earns, please provide those details, and I can help you calculate it more precisely!
1. **Determine the Cost of the Jacket**: Let's say the jacket costs \( P \) dollars.
2. **Find Out How Much Riley Can Earn**: We need to know how much money Riley earns per hour or per task. For instance, if Riley earns \( E \) dollars per hour, that means Riley can earn in a proportional relationship based on the time worked.
3. **Set Up the Proportional Relationship**:
- If \( H \) is the number of hours Riley can work, the total earnings can be expressed as:
\[
\text{Total Earnings} = E \times H
\]
- To ensure Riley can buy the jacket, set up the inequality:
\[
E \times H \geq P
\]
4. **Solve for Hours Needed**:
Rearranging the inequality gives:
\[
H \geq \frac{P}{E}
\]
This formula shows how many hours Riley needs to work to afford the jacket.
### Example:
Assume:
- The jacket costs \( P = 80 \) dollars.
- Riley earns \( E = 10 \) dollars per hour.
Using the formula:
\[
H \geq \frac{80}{10} = 8
\]
So, Riley needs to work at least 8 hours to earn enough money to purchase the jacket.
If you have specific numbers for the cost of the jacket and how much Riley earns, please provide those details, and I can help you calculate it more precisely!
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