Finding students wearing hats but not scarves

[the4thcafeavenue]

such an easy math problem but i can't do it! help!

a group of 20 students is waiting for the school bus. each child is wearing either a hat, a scarf, or both. if 10 wear hats and 16 wear scarves, how many are wearing hats but no scarves?

it seems so easy buh it's quite annoying.
help. thnks.

 

[t!m]

Ask yourself how many students are NOT wearing scarves, and then think about what that implies.

 

[Curious3141]

For starters, draw a Venn diagram, it should be clearer.

Just let the no. of students with hats alone be A, with scarves alone be C and the ones with both be B.

Can you set up 3 simple simultaneous equations in A, B and C ? Then solve for A by substitution.

That's one way. The other is to use the well known equation from set theory :

n(Hats Union Scarves) = n(Hats) + n(Scarves) - n(Hats IntersectionScarves)

Sorry, I don't know how to represent that in LaTeX symbols. The left hand side is the total number of students (given to be twenty). You know two terms in the RHS. Find the number of the intersection and then figure out how many students wear only hats and no scarves.