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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 :
(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 ?
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 ?
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Sol. (i) $5x + 4y = 9500$
dots (1)
$4x + 3y = 7370$
dots (2)
(ii) (a) Solving (1) and (2), $x = 980$
$\therefore$ Prize Amount for Hockey = ₹$980$
OR
(ii) (b) On solving $x = 980, y = 1,150$
$\therefore$ Prize Amount for Cricket is more by ₹$(1,150 – 980) = \text{Rs} 170$
(iii) $2(x + y) = 2(980 + 1150) = 2(2130) = \text{Rs} 4,260$
dots (1)
$4x + 3y = 7370$
dots (2)
(ii) (a) Solving (1) and (2), $x = 980$
$\therefore$ Prize Amount for Hockey = ₹$980$
OR
(ii) (b) On solving $x = 980, y = 1,150$
$\therefore$ Prize Amount for Cricket is more by ₹$(1,150 – 980) = \text{Rs} 170$
(iii) $2(x + y) = 2(980 + 1150) = 2(2130) = \text{Rs} 4,260$