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

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

Ans:

(i) Making equations:

From the given information, we get the following equations:

5 x + 4 y = 9500………….(i)

4 x + 3 y = 7370..……….(ii)

(ii) (a) Prize amount for hockey: we need to find the value of x

By solving equations (i) and (ii), we get

15x – 16x = 28,500 – 29480 = – 980

x = 980

(ii) (b) Higher prize money: we need to find higher of x & y

Let’s substitute value of x in equation (i), we get:

5 (980) + 4 y = 9500

4 y = 9500 – 4900 = 4600

y = 1150

Difference between prize money: y – x = 1150 – 980 = 170 per student

Clearly, we can see that y (or prize money for cricket) is higher by Rs. 170

(iii) Prize money for 2 students:

if 2 students get prize money for both games, then prize money = 2 (x + y)

= 2 (980 + 1150) = 4,260

Therefore, the total prize money will be Rs. 4,260.