Advertisements
Advertisements
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?
Advertisements
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
APPEARS IN
RELATED QUESTIONS
Form the pair of linear equation in the following problem, and find its solution (if they exist) by the elimination method:
The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.
In an envelope there are some 5 rupee notes and some 10 rupee notes. Total amount of these notes together is 350 rupees. Number of 5 rupee notes are less by 10 than twice number of 10 rupee notes. Then find the number of 5 rupee and 10 rupee notes.
Solve the following simultaneous equation.
`x/3 + 5y = 13 ; 2x + y/2 = 19`
By equating coefficients of variables, solve the following equation.
5x + 7y = 17 ; 3x - 2y = 4
A fraction becomes `1/3` when 2 is subtracted from the numerator and it becomes `1/2` when 1 is subtracted from the denominator. Find the fraction.
If 52x + 65y = 183 and 65x + 52y = 168, then find x + y = ?
Complete the following table to draw the graph of 3x – 2y = 18.
| x | 0 | 4 | 2 | –1 |
| y | –9 | ______ | ______ | ______ |
| (x, y) | (0, −9) | (______, _______) | (______, _______) | ______ |
Difference between two numbers is 3. The sum of three times the bigger number and two times the smaller number is 19. Then find the numbers.
The sum of the digits of a two-digit number is 9. If 27 is added to it, the digits of the number get reversed. The number is ______.
Rehana went to a bank to withdraw ₹ 2000. She asked the cashier to give her ₹ 50 and ₹ 100 notes only. Rehana got 25 notes in all. Find how many notes of ₹ 50 and ₹ 100 did she received.
