Draw a venn diagram to illustrate the following. In a shop 50 cars were inspected and it found that 23 needed new brakes and 34 needed new tires. 3 needed no services at all how many needed new brakes and new tires? How many only needed brakes? Please help
label the intersection of the two circles as x
so the 23 includes the x and the 34 includes the x
equation:
50 = 23 + 34 - x + 3
x = 10
so 10 needed both brakes and tires, so
13 needed only brakes
To answer this question, let's create a Venn diagram step-by-step:
Step 1: Start by drawing a rectangle to represent the universe, which, in this case, is the total number of cars inspected in the shop (50 cars).
Step 2: Label the different categories you want to represent. In this case, we will label them as "New Brakes," "New Tires," and "No Services."
Step 3: Let's fill in the information we have. We know that there were 23 cars that needed new brakes, 34 cars that needed new tires, and 3 cars that needed no services at all.
Step 4: Place the numbers in the corresponding areas of the Venn diagram. Since we are dealing with overlapping categories, we should place the numbers in the overlapping regions as well.
Based on the information provided, we can determine the numbers for each section:
- "New Brakes" (23 cars): This represents cars that need new brakes, regardless of whether they also need new tires.
- "New Tires" (34 cars): This represents cars that need new tires, regardless of whether they also need new brakes.
- "Both New Brakes and New Tires" (unknown): This represents the overlap region where cars need both new brakes and new tires.
- "No Services" (3 cars): This represents cars that need no services at all.
Since we don't know the exact number of cars that need both new brakes and new tires, we will denote it with the letter 'x.' This is what we need to find.
Now, let's calculate the values for the missing sections:
- "Both New Brakes and New Tires" (x cars): This represents cars that need both new brakes and new tires. To calculate this value, we can use the formula: Total = New Brakes + New Tires - Both (the overlapping region). Inserting the known values, we have the equation: 50 = 23 + 34 - x. Solving for x, we find x = 7.
- "Only Needed Brakes" (16 cars): This represents cars that need new brakes but not new tires. To calculate this value, we need to subtract the overlapping region from the total number in the "New Brakes" category. We have: Only Needed Brakes = New Brakes - Both = 23 - 7 = 16.
To summarize the results in the Venn diagram:
________________
| |
| 7 cars |
|________________|
| |
16 cars | | 27 cars
(Only | | (Only
Brakes) | Both | Tires)
| 7 cars |
|________________|
| |
| 3 cars |
|________________|
So, according to the Venn diagram, there are 7 cars that need both new brakes and new tires, and there are 16 cars that only need new brakes.