Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

Some History teachers at Washington High School are purchasing tickets for students and their adult chaperones to go on a field trip to a nearby museum. For her class, Mrs. Yamada bought 31 student tickets and 25 adult tickets, which cost a total of $673. Mr. Blair spent $707, getting 31 student tickets and 27 adult tickets. What is the price for each type of ticket?

Answer 1

Adults $ 17

Students: $8

Explanation:

Adults: x

Students: y

a) 25x + 31y = 673

b) 27x +31y = 707

Elimination:

a) -1(25x + 31y = 673) = -25 -31y = -673

a + b

= (-25 -31y = -673) + (27x + 31y = 707)

= 2x = 34

x = 34/2

x = 17

Substitution a or b:

a) 25(17) + 31y = 673

425 + 31y = 673

31y = 673 - 425

31y = 248

y = 248/31

y = 8