For a certain shade of pink paint, the ratio of white paint to red paint is 5 to 2. Explain how to use the strip diagram shown below to find at least 6 different quantities of white and red paint that will be in the ratio 5 to 2 (and so will make the same shade of pink). In each case, describe the amount of pink paint that will be made. Include at least 3 mixtures where the quantities of paint are not both whole numbers of units. (You may choose any units you like, such as gallons, liters, pails, or something else.)
I’m stuck with this problem. Can someone please help me with this problem?
Again, no diagram.
To use the strip diagram to find different quantities of white and red paint in the ratio 5 to 2, and to determine the amount of pink paint that will be made, follow these steps:
1. Start by drawing a horizontal line to represent the total amount of paint. Divide this line into seven equal sections, as shown in the strip diagram.
2. Label the leftmost section as "White" and the next section as "Red." These labels represent the quantities of white paint and red paint, respectively.
3. Since the ratio of white paint to red paint is 5 to 2, divide the "White" section into five equal parts and the "Red" section into two equal parts. These divisions represent the ratio between the two colors.
4. Each part of the "White" section represents one unit of white paint, and each part of the "Red" section represents one unit of red paint.
5. To find the different quantities of white and red paint that will be in the ratio 5 to 2, choose any number of units (whole or fractional) for the white paint and multiply it by five. Then, choose a number of units (whole or fractional) for the red paint and multiply it by two.
6. For example, let's say you choose 5 units of white paint. Multiply 5 by 5, which gives you 25 units of white paint. Then, choose 2 units of red paint. Multiply 2 by 2, which gives you 4 units of red paint.
7. To determine the amount of pink paint that will be made, add the quantities of white and red paint together. In this case, 25 units of white paint plus 4 units of red paint equals 29 units of pink paint.
8. Repeat this process to find at least 6 different quantities of white and red paint that will be in the ratio 5 to 2. You can choose different numbers of units for each color to explore various combinations.
For instance, you can choose 7 units of white paint and 2.8 units of red paint. 7 multiplied by 5 is 35, and 2.8 multiplied by 2 is 5.6. This results in a total of 40.6 units of pink paint.
Remember, the strip diagram helps provide a visual representation of the ratio between the two colors, allowing you to explore different combinations and quantities while maintaining the ratio.