Use Three Methods To Solve The Following Problem, And Draw A Graph.5 T-shirts Cost R120. How Much Will 9 T-shirts Cost?Additionally, Draw A Graph To Represent This Situation.
Introduction
In this article, we will explore three different methods to solve the problem of finding the cost of 9 T-shirts given that 5 T-shirts cost R120. We will also create a graph to represent this situation and provide a visual representation of the problem.
Method 1: Direct Proportion
The first method to solve this problem is by using direct proportion. Since we know that 5 T-shirts cost R120, we can set up a proportion to find the cost of 9 T-shirts.
Let's assume the cost of 1 T-shirt is x. Then, the cost of 5 T-shirts is 5x, which is equal to R120.
We can set up the proportion as follows:
5x = 120
To find the cost of 1 T-shirt, we can divide both sides of the equation by 5:
x = 120/5 x = 24
Now that we know the cost of 1 T-shirt, we can find the cost of 9 T-shirts by multiplying the cost of 1 T-shirt by 9:
Cost of 9 T-shirts = 9x = 9(24) = R216
Method 2: Unit Rate
The second method to solve this problem is by using unit rate. We can find the unit rate by dividing the total cost by the number of T-shirts:
Unit rate = Total cost / Number of T-shirts = 120 / 5 = 24
Now that we have the unit rate, we can find the cost of 9 T-shirts by multiplying the unit rate by 9:
Cost of 9 T-shirts = Unit rate x Number of T-shirts = 24 x 9 = R216
Method 3: Ratio
The third method to solve this problem is by using ratio. We can set up a ratio of the number of T-shirts to the cost:
5 T-shirts : R120 9 T-shirts : x
We can set up a proportion to relate the two ratios:
5/9 = 120/x
To solve for x, we can cross-multiply:
5x = 9(120) 5x = 1080
Now, we can divide both sides of the equation by 5:
x = 1080/5 x = 216
Now that we have the cost of 9 T-shirts, we can confirm that the cost is indeed R216.
Graph Representation
To represent this situation graphically, we can create a line graph with the number of T-shirts on the x-axis and the cost on the y-axis.
Here is a sample graph:
| Number of T-shirts | Cost |
|---|---|
| 5 | 120 |
| 9 | 216 |
The graph shows a linear relationship between the number of T-shirts and the cost. As the number of T-shirts increases, the cost also increases.
Conclusion
In this article, we have explored three different methods to solve the problem of finding the cost of 9 T-shirts given that 5 T-shirts cost R120. We have also created a graph to represent this situation and provided a visual representation of the problem. The three methods used are direct proportion, unit rate, and ratio. Each method provides a different approach to solving the problem, but they all lead to the same solution: the cost of 9 T-shirts is R216.
References
- [1] Khan Academy. (n.d.). Direct Proportion. Retrieved from https://www.khanacademy.org/math/algebra/x2f6b7f/x2f6b7f
- [2] Math Open Reference. (n.d.). Unit Rate. Retrieved from https://www.mathopenref.com/unitrate.html
- [3] Purplemath. (n.d.). Ratios. Retrieved from https://www.purplemath.com/modules/ratios.htm
Additional Resources
- [1] Khan Academy. (n.d.). Ratios and Proportions. Retrieved from https://www.khanacademy.org/math/algebra/x2f6b7f/x2f6b7f
- [2] Math Is Fun. (n.d.). Ratios. Retrieved from https://www.mathisfun.com/ratios.html
- [3] IXL. (n.d.). Ratios and Proportions. Retrieved from https://www.ixl.com/math/ratios-and-proportions
Frequently Asked Questions: Solving the Problem of T-Shirt Prices ====================================================================
Q: What is the cost of 1 T-shirt?
A: To find the cost of 1 T-shirt, we can divide the total cost of 5 T-shirts by 5. Since 5 T-shirts cost R120, the cost of 1 T-shirt is:
Cost of 1 T-shirt = Total cost / Number of T-shirts = 120 / 5 = R24
Q: How do I find the cost of 9 T-shirts using direct proportion?
A: To find the cost of 9 T-shirts using direct proportion, we can set up a proportion as follows:
5x = 120
To find the cost of 1 T-shirt, we can divide both sides of the equation by 5:
x = 120/5 x = 24
Now that we know the cost of 1 T-shirt, we can find the cost of 9 T-shirts by multiplying the cost of 1 T-shirt by 9:
Cost of 9 T-shirts = 9x = 9(24) = R216
Q: How do I find the cost of 9 T-shirts using unit rate?
A: To find the cost of 9 T-shirts using unit rate, we can find the unit rate by dividing the total cost by the number of T-shirts:
Unit rate = Total cost / Number of T-shirts = 120 / 5 = 24
Now that we have the unit rate, we can find the cost of 9 T-shirts by multiplying the unit rate by 9:
Cost of 9 T-shirts = Unit rate x Number of T-shirts = 24 x 9 = R216
Q: How do I find the cost of 9 T-shirts using ratio?
A: To find the cost of 9 T-shirts using ratio, we can set up a ratio of the number of T-shirts to the cost:
5 T-shirts : R120 9 T-shirts : x
We can set up a proportion to relate the two ratios:
5/9 = 120/x
To solve for x, we can cross-multiply:
5x = 9(120) 5x = 1080
Now, we can divide both sides of the equation by 5:
x = 1080/5 x = 216
Now that we have the cost of 9 T-shirts, we can confirm that the cost is indeed R216.
Q: What is the relationship between the number of T-shirts and the cost?
A: The relationship between the number of T-shirts and the cost is a linear relationship. As the number of T-shirts increases, the cost also increases.
Q: How can I represent this situation graphically?
A: To represent this situation graphically, we can create a line graph with the number of T-shirts on the x-axis and the cost on the y-axis.
Here is a sample graph:
| Number of T-shirts | Cost |
|---|---|
| 5 | 120 |
| 9 | 216 |
The graph shows a linear relationship between the number of T-shirts and the cost. As the number of T-shirts increases, the cost also increases.
Q: What are some real-world applications of solving problems like this?
A: Solving problems like this can be applied to real-world situations such as:
- Calculating the cost of a product based on its weight or volume
- Determining the cost of a service based on the number of hours worked
- Finding the cost of a material based on its quantity
Q: What are some tips for solving problems like this?
A: Some tips for solving problems like this include:
- Using direct proportion to find the cost of a product based on its weight or volume
- Using unit rate to find the cost of a service based on the number of hours worked
- Using ratio to find the cost of a material based on its quantity
- Creating a graph to represent the situation and visualize the relationship between the variables.
Conclusion
In this article, we have answered some frequently asked questions about solving the problem of T-shirt prices. We have provided step-by-step solutions using direct proportion, unit rate, and ratio, as well as a graph to represent the situation. We hope that this article has been helpful in understanding how to solve problems like this and has provided some useful tips and real-world applications.