Question

Two schools 'X' and 'Y' decided to award prizes to their students for two games—₹p per student for hockey and ₹q per student for cricket. School X decided to award a total of ₹ 9500 for the two games to 5 and 4 students respectively; while school Y decided to award ₹ 7370 for the two games to 4 and 3 students respectively.

Based on the above information, answer the following questions.

1. Represent the above information algebraically (in terms of p and q). 
2. What is the prize amount for hockey? 
3. Prize amount for which game is higher and by how much? 
4. What will be the total prize amount if there are 2 students each from the two games?

Answer 1

i. School X: \[5p + 4q = 9500\] 

School Y: \[4p + 3q = 7370\] 

ii. Multiply the first equation by 3 and the second by 4:

\[15p + 12q = 28500\] 

\[16p + 12q = 29480\] 

Subtracting: \[p = 980\] 

Substituting: \[4q = 9500 - 4900 = 4600 \Rightarrow q = 1150\] 

Prize for hockey = ₹980. 

iiii. Cricket prize is higher by \[1150 - 980 = ₹170\] 

iv. Total prize for 2 students in each game: \[2 \times (980 + 1150) = ₹4260\]