use proportional relationships to solve the following problem riley needs to earn enough money to purchas a new jacket

1 answer

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!