Question

PLEASE TELL ME HOW TO EVEN START THIS ?:


Paula is a big fan of the great 20th-century Russian composers. Examining her collection of 24 albums, a quick survey found the following:


Paula has 5 albums that feature compositions by both Stravinsky and Prokofiev.
Paula has 6 albums that only feature compositions by Stravinsky.
Paula has 7 albums that feature compositions by Prokofiev.

a) How many albums in Paula’s collection only feature compositions by Prokofiev?

b) How many albums albums in Paula’s collection feature no compositions by either Stravinsky or Prokofiev?

Answer 1

Do you know what a Venn diagram is?

Answer 2

Nice! So how would you set one up for this problem?

Answer 3

You only need two circles, and 24 is the total so the numbers should add up to 24. This so far is good:

Answer 4

Think of the outside of all the circles as "Has neither S nor P."

Answer 5

so it would be 24-5-6-X

Answer 6

Ok, and what should X be? How do we use the fact that 7 albums feature Prokofiev?

Answer 7

Everything in P should add up to 7.

Answer 8

2 i ment

Answer 9

x = 11

Answer 10

Perfect!

Answer 11

so a =2 and b=11 ?

Answer 12

Exactly.

Answer 13

great thanks so much!

Answer 14

You're welcome!