Question

Read the following passage:

Two schools 'P' and 'Q' decided to award prizes to their students for two games of Hockey ₹ x per student and Cricket ₹ y per student. School 'P' decided to award a total of ₹ 9,500 for the two games to 5 and 4 Students respectively; while school 'Q' decided to award ₹ 7,370 for the two games to 4 and 3 students respectively.

Based on the above information, answer the following questions:

1. Represent the following information algebraically (in terms of x and y).
2. (a) What is the prize amount for hockey?
   OR
   (b) Prize amount on which game is more and by how much?
3. What will be the total prize amount if there are 2 students each from two games?

Answer 1

i. Given, Hockey ₹ x per student and Cricket ₹ y per students

∴ Algebraic equations are

5x + 4y = 9500             ...(i)

and 4x + 3y = 7370     ...(ii)

ii. (a) Multiply by 3 in equation (i) and by 4 in equation (ii)

15x + 12y = 28,500      ...(iii)

16x + 12y = 29480       ...(iv)

On subtracting equation (iii) from equation (iv), we get

x = 980

∴ Prize amount for hockey = ₹ 980

OR

(b) Now, put this value in equation (i), we get

5 × 980 + 4y = 9500

`\implies` 4y = 9500 – 4900 = 4600

`\implies` y = 1150

∴ Prize amount for cricket = ₹ 1150

Difference = 1150 – 980 = 170

∴ Prize amount for cricket is ₹ 170 more than hockey.

iii. Total prize amount for 2 students each from two games

= 2x + 2y

= 2(x + y)

= 2(980 + 1150)

= 2 × 2130

= ₹ 4260