In a group of 12 chefs, all enjoy baking cakes and/or tarts. In fact, 7 enjoy baking cakes and 8 enjoy baking tarts. Find out how many chefs enjoy baking both cakes and tarts.
Ans = 3, i'm having trouble figuring out how to get this answer. Any help is appreciated.
draw Venn diagram
c = 7
t = 8
intersection = i
c-i + t = 12
15 - i = 12
i = 3
so
4 cake only and 5 tart only and 3 both
thanks
Thanks so much!!
cc
Well, let's see if we can solve this delicious conundrum. We know that there are 12 chefs in total, and that 7 of them enjoy baking cakes and 8 enjoy baking tarts.
Now, we can assume that "enjoying baking cakes" and "enjoying baking tarts" are not mutually exclusive. In other words, some chefs might enjoy baking both cakes and tarts at the same time.
To find out how many chefs enjoy baking both cakes and tarts, we can try using a simple formula:
Number of chefs who enjoy baking both cakes and tarts = Number of chefs who enjoy baking cakes + Number of chefs who enjoy baking tarts - Total number of chefs.
Plugging in the values, we have:
Number of chefs who enjoy both cakes and tarts = 7 + 8 - 12.
And what does that give us? Well, simple math, my friend. 7 + 8 equals 15, and when you subtract 12 from that, you get... drumroll, please... 3!
So, it seems that 3 chefs in this group of 12 enjoy the best of both worlds, baking both cakes and tarts. I guess you could call them "culinary multitaskers" or "bakers extraordinaire."
To find out how many chefs enjoy baking both cakes and tarts, you can use the concept of sets and intersections. Let's break it down:
1. Start by understanding the information given:
- Total number of chefs: 12
- Number of chefs who enjoy baking cakes: 7
- Number of chefs who enjoy baking tarts: 8
2. Represent the sets:
- Let's represent the set of chefs who enjoy baking cakes as Set A.
- Let's represent the set of chefs who enjoy baking tarts as Set B.
3. Use the intersection to find the number of chefs who enjoy both cakes and tarts:
- The intersection of Set A and Set B represents the chefs who enjoy both cakes and tarts.
- Mathematically, the intersection is denoted by A ∩ B.
4. Substituting the given values, we have:
- A = 7 (chefs who enjoy baking cakes)
- B = 8 (chefs who enjoy baking tarts)
- A ∩ B = ?
5. To find the intersection using the given information:
- Since 7 chefs enjoy baking cakes and 8 enjoy baking tarts, we can conclude that at most 7 + 8 = 15 chefs enjoy cakes and/or tarts (assuming there are no chefs who don't enjoy either).
- However, we know that there are only 12 chefs in total. So, the maximum number of chefs who can enjoy both cakes and tarts is limited to 12.
6. Calculating the intersection:
- To calculate A ∩ B, we subtract the number of chefs who enjoy either cakes or tarts (15) from the total number of chefs (12) to account for the double-counted chefs.
- A ∩ B = 12 - 15 = -3
7. Interpretation of the result:
- The negative result (-3) indicates that there might be an error or overlap in the given information. In this case, it suggests that the given values are not consistent or accurate.
Based on the calculations, it seems that the given numbers do not add up correctly, and it's not possible to determine the exact number of chefs who enjoy both cakes and tarts.