There are 500 kids at my school. 20% have frogs and 30% have fish. 27 kids have both. How many have neither?
I thought the answer was 250 kids but my teacher said that was wrong. Help!
Thanks,
Taylor
If you do
500 - (0.2*500 + 0.3*500) = 250
Then you have subtracted the kids who only have frogs correctly and the kids who only have fish correctly. But the kids who have both have been subtracted twice, because they are part of the 0.2*500 = 100 kids who have fish and also the 0.3*500 = 150 kids who have fish.
So, to correct for the fact that these have been subtracted twice you have to add the 27 who have both.
The question is confusing. It isn't clear whether the 27 kids are included in the 50% who have frogs and/or fish. Since 250 is wrong, then we need to add 27 to 250 to find that 277 kids have frogs and/or fish. That leaves 223 who have neither.
Okay thanks this helps!
I have a feeling that they want you to do this with Venn diagrams.
Usually this type is done this way:
Draw a rectangle with two intersecting circles inside the rectangle.
Label one circle Frogs and the other Fish.
Put the number 27 in the region where they intersect.
Now in the Fish circle you are supposed to have 30% of 500, or 150, but you have already 27 in that circle, so put 123 in the open part of that circle.
Now in the Frog circle, which is to contain 100, with 27 already entered, put 73 in the open part of that circle.
The entries found inside the whole rectangle should be 500.
So far we have entered 27+123+73 or 223 inside our circles, so put 277 inside the rectangle but outside of the circles.
These 277 represent the students who have neither fish nor frogs.
To find the number of kids who have neither frogs nor fish, we need to subtract the total number of kids who have either frogs or fish from the total number of kids at the school.
First, we need to find the number of kids who have either frogs or fish.
Let's start with the number of kids who have frogs. If 20% of the 500 kids have frogs, we can calculate it by multiplying:
20% * 500 = (20/100) * 500 = 0.2 * 500 = 100
So, 100 kids have frogs.
Next, let's find the number of kids who have fish. If 30% of the 500 kids have fish, we can calculate it in a similar way:
30% * 500 = (30/100) * 500 = 0.3 * 500 = 150
So, 150 kids have fish.
However, we also know that 27 kids have both frogs and fish. If we add these two numbers together, we'll be counting these 27 kids twice, so we need to subtract them once:
100 + 150 - 27 = 250
So, 250 kids have either frogs or fish.
Now, to find the number of kids who have neither frogs nor fish, we subtract this from the total number of kids at the school:
500 - 250 = 250
Therefore, the correct answer is that 250 kids have neither frogs nor fish.
If your teacher said this answer was wrong, it's a good idea to clarify with them to understand why they marked it as incorrect.