car A costs 20 percent less than car B. Car B costs twice as much as Car C. The cost of Car C is what percent of the cost of Car A?
How do I set up this question? What should the process of thinking be for these questions?
A = B - 20 % B = B - 0.2 B = 0.8 B
A = 0.8 B Divide both sides by 0.8
A / 0. 8 = 0.8 B / 0.8
1.25 A = B
B = 1.25 A
B = 2 C Divide both sides by 2
B / 2 = C
C = B / 2
C = 1.25 A / 2
C = 0.625 A = 0.625 A * 100 /100 = 62.5 % A
Thank you! But does this have anything to do with ratios?
To set up this question, it's important to break it down into smaller steps and consider the relationships between the prices of the cars:
1. Let's assign variables to represent the costs of each car. Let's say car A costs A dollars, car B costs B dollars, and car C costs C dollars.
2. Given that car A costs 20 percent less than car B, we can write the equation A = B - 0.2B, or A = (1 - 0.2)B, which simplifies to A = 0.8B.
3. Next, we know that car B costs twice as much as car C. So, we can write the equation B = 2C.
4. Now, we need to express the cost of car C as a percentage of the cost of car A. To do this, we need to find the ratio of C to A.
5. Substituting the value of B from equation 3 into equation 2, we get A = 0.8(2C) or A = 1.6C.
6. To express the cost of car C as a percentage of car A, we need to calculate the ratio C/A and multiply it by 100%. So, the percentage can be calculated as (C/A) * 100%.
Now, let's go through the thinking process for solving these types of questions:
1. Understand the given information: Read the problem carefully and identify the key information provided. In this case, we know that car A costs 20% less than car B, and car B costs twice as much as car C.
2. Define variables: Assign variables to represent the unknown quantities. It's common to use letters like A, B, C to represent different items or amounts.
3. Establish equations: Write equations that incorporate the given information and the relationships between the variables.
4. Simplify the equations: Manipulate the equations algebraically to express one variable in terms of another, if possible.
5. Solve for the required information: Use the equations to find the value or relationship being asked for in the question.
6. Check your answer: Verify that your answer makes sense and is consistent with the given information.
By following these steps, you can more easily understand and solve complex word problems involving relationships between quantities or variables.