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