I need word problem HELPPPPPP

Question

In a large high school, some teachers teach only 1 subject, and some teach more than 1 subject.  Using the information given about the math, science and gym teachers in the school, how many teachers teach math only?

 

12 teachers teach at least one class of math

10 at least one class of gym

20 at least one class of science

6 both gym and science but not gym

2 gym only

1 math, gym and science

Answer 1

There is information missing and that what is typed is not entirely correct...

For example, the fourth statement is incorrect

6 both gym and science but not gym"

You perhaps meant 6 both gym and science but not math...

Assuming that, set up a Venn Diagram with three circles: math, gym, and science...

2 teach only gym, 6 teach gym and science, and 1 teaches all 3...

since 10 teach gym altogether, that leaves 1 to teach gym and math...

Let y be the number that teaches science and math...

then, since 20 teach science, the number of science only is 13-y

and number of math only is 10-y

We need one of the following to finish the problem:

number of math and science OR

total science OR

total math OR

total # of teachers altogether