Why do linear pairs have to be adjacent?

Prove that 3: 8 is equivalent to 12: 32.a. use diagrams to support your answer.

Cassie is traveling 675 miles today to visit her brother and his family. so far, she has stopped for gas three times. at the first stop, she put in 7.1 gallons of gas and paid $23.79. at her second stop, she put in 5.8 gallons of gas and paid $19.08. and, at the third stop, 6.6 gallons and paid $20.39. at which stop did casey pay the most for gas?

Mrs. morton has a special reward system for her class. when all her students behave well, she rewards them by putting 3 marbles into a marble jar. when the jar has 100 or more marbles, the students have a party. right now, the the jar has 24 marbles. how could mrs. morton reward the class in order for the students to have a party?