Question

30. Two families go to the movies. One family purchases two adult tickets and four youth tickets for $46.

Another family purchases three adult tickets and five youth tickets for $62. How much would it cost to
purchase six adult tickets and eight youth tickets?

Answer 1

adult’s ticket is $9

youth’s ticket is $7

Explanation:

let x = adult’s ticket

let y = youth’ ticket

first family

2x + 4y = 46 Eq.1

another family

3x + 5y = 62. Eq.2

Multiply eq.1 by -3 and eq.2 by 2

-3(2x + 4y = 46)

-6x - 12y = -138 Eq.3

2(3x + 5y = 62)

6x + 10y = 124 Eq.4

add Eq.3 & Eq.4

-6x - 12y = -138

6x + 10y = 124

————————-

-2y = - 14

y = $7

to get the value of x, substitute y = 7 to any of the equations

2x + 4y = 46

2x + 4(7) = 46

2x + 28 = 46

2x = 18

x = $9