Question

82. Four tickets for movie A and five tickets for movie B cost 1540 but five tickets for movie A
and four tickets for movie B cost 1460. What is the cost of the tickets for movie B?
(1) 2450
(2) 400
(3) 333.34
4) 206.67
​

Answer 1

Answer:

(4) 206.67

Step-by-step explanation:

let cost of 1 ticket for movie A be x and cost of 1 ticket of movie B is y

now 4 tickets for movie A and 5 tickets for movie B cost 1540

therefore, 4x + 5y = 1540 ....(1)

also 5 tickets for movie A and 4 tickets for movie B cost 1460

therefore, 5x + 4y = 1460 ....(2)

adding equation (1) and (2)

(4x + 5y) + (5x + 4y) = 1540 + 1460

9x + 9y = 3000

9(x+y) = 3000

3(x+y) = 1000 ....(3)

subtracting equation (1) and (2)

(4x + 5y) - (5x + 4y) = 1540 - 1460

4x - 5x + 5y - 4y = 80

- x + y = 80

y = 80 + x ....(4)

placing value of y in (3)

3(x + (80 + x)) = 1000

3(2x + 80) = 1000

6x + 240 = 1000

6x = 1000 - 240

6x = 760

x = 126.67

placing value of x in (4)

y = 80 + 126.67 = 206.67

therefore, the cost of ticket of movie B is 206.67