Answer to Question #237444 in Algebra for Mr. Lee

Question

A survey of seventy‐one students reveals that 50 take the

jeepney. 36 take the bus 33 take the tram 20 take the

jeepney and the bus 18 take the bus and the train 22 take

the train and the jeepney 12 take the jeepney. bus and the

train

How many students take the jeepney only? How many

students take the bus only? .1 How many students take the

train only?

Answer 1

We can solve this problem using venn-diagram

Total students of jeepney=50

students of jeepney=only jeepney+(Bus of jeepney)+(jeepney+Train)+(jeepney+bus+train)

$50=only \space jeepney+20+22+12$

Students only of jeepney$=50-42+12=20$

Students only of bus $=36-(20+18)+12=10$

students of only train$=33-(22+18)+12=5$