Question

At marina two types of games viz., Horse riding and Quad Bikes riding are available on hourly rent. Keren and Benita spent ₹ 780 and ₹ 560 during the month of May.

Name	Number of hours		Total amount spent (in ₹)
	Horse Riding	Quad Bike Riding
Keren	3	4	780
Benita	2	3	560

Find the hourly charges for the two games (rides). (Use determinant method)

Answer 1

Let the hourly charges for horse riding be x and let the hourly charges for Quad Bikes riding be y.

For Keren

3x + 4y = 780  ........(1)

For Benita

2x + 3y = 560  ........(2)

Here Δ = `|(3, 4),(2, 3)|`

= 9 – 8

= 1 ≠ 0

∴ We can apply Cramer’s Rule

Now `Delta_x = |(780, 4),(560, 3)|`

= 2340 – 2240

= 100

`Delta_y = |(3, 780),(2, 560)|`

= 1680 – 1560

= 120

∴ By Cramer's rule

x = `Delta_x/Delta = 100/1` = 100

y = `Delta_y/Delta = 120/1` = 120

∴ The hourly charges for horse riding is ₹ 100 and Quad Bikes riding is ₹ 120