Use porpotinoal relationships to solve the following problems Riley needs to earn enough money to purchase a new jacket
To solve this problem using proportional relationships, we need to assume that the amount of money Riley needs to earn is directly proportional to the cost of the new jacket.
Let's define the variables:
- Let C be the cost of the new jacket in dollars.
- Let M be the amount of money Riley needs to earn to purchase the jacket in dollars.
Since the relationship between the cost of the jacket and the amount of money needed is proportional, we can write the equation:
M = kC
Where k is the constant of proportionality.
To solve for k, we need to know a pair of values for M and C. Let's assume that Riley needs to earn $200 to purchase a jacket that costs $100. Substituting these values into the equation, we get:
200 = k * 100
Dividing both sides by 100, we find:
k = 2
Now that we have the value of k, we can use this equation to find the amount of money Riley needs to earn for any given cost of a jacket. Let's say Riley wants to purchase a jacket that costs $150. Substitute C = 150 into the equation, and solve for M:
M = 2 * 150
M = 300
Therefore, Riley needs to earn $300 to purchase a jacket that costs $150.
Step 1: Determine the price of the new jacket that Riley wants to purchase. Let's say the price of the jacket is $100.
Step 2: Identify the amount of money Riley currently has. Let's say Riley has $50.
Step 3: Calculate the remaining amount of money that Riley needs to earn. This can be done by subtracting the current amount of money Riley has from the price of the jacket. In this case, $100 - $50 = $50.
Step 4: Divide the remaining amount Riley needs to earn by the amount of money Riley currently earns for each task. This will give you the number of tasks Riley needs to complete to earn enough money for the jacket.
Step 5: Let's say Riley earns $10 for each task completed. Divide the remaining amount needed by the amount earned per task: $50 / $10 = 5.
Step 6: The result from Step 5 indicates that Riley needs to complete 5 tasks to earn enough money for the jacket.
To solve problems related to proportional relationships, we need to understand the concept of proportionality. In a proportional relationship, two variables have a constant ratio. This means that if one variable increases or decreases, the other variable will also increase or decrease in the same proportion.
Now, let's apply this concept to Riley's situation. To earn enough money to purchase a new jacket, we need to consider the following factors:
1. Cost of the jacket: Determine the total cost of the desired jacket. Let's say it costs $100.
2. Time/work ratio: Determine how much time or work Riley needs to put in to earn a certain amount of money. For example, if Riley earns $10 per hour for part-time work, he would need to work 10 hours to earn $100.
3. Proportional relationship: Establish a proportional relationship between the time/work and the amount of money earned. In this case, the ratio is 1:10. That means for every hour Riley works, he earns $10.
4. Calculate the required time/work: To figure out how much time/work Riley needs to earn enough money, set up a proportion where x represents the required time/work, and solve for x:
x hours / $10 = 10 hours / $100
Cross-multiply and solve for x:
10x = 10 * $10
10x = $100
x = $100 / 10
x = 10 hours
Therefore, Riley needs to work 10 hours to earn enough money to purchase the $100 jacket based on the given proportions.