EXERCISE 3E
1. 5 chairs and 4 tables together cost * 2800 while 4 chairs and 3 tables
together cost 2170. Find the cost of a chair and that of a table.
237 pens and 53 pencils together cost 820 while 53 pens and 37 pencils
together cost 980. Find the cost of a pen and that of a pencil.
3. A lady has only 20-paisa coins and 25-paisa coins in her purse. If she
has 50 coins in all totalling * 11.50, how many coins of each kind does
she have?
4. The sum of two numbers is 137 and their difference is 43. Find
the numbers.
5. Find two numbers such that the sum of twice the first and thrice th
second is 92, and four times the first exceeds seven times the secon
by 2.
Answers
Answer:
Step-by-step explanation:
1. Let the cost of chair be x and table be y
given
5 x + 4 y = 2800 ........(1)
4 x + 3y = 2170 .........(2)
on solving (1) & (2)
x = 280 , y = 350
cost of chair = Rs. 280
cost of tables = Rs. 350
2. cost of pen and pencil be x and y respectively
given
37 x + 53 y = 820 ........(1)
53 x + 37 y = 980 ....(2)
(1) + (2)
90 x + 90 y = 1800
x + y = 20 .......(3)
(1) - (2)
- 16 x + 16 y = - 160
- x + y = - 10 ........(4)
on solving (3 ) & (4)
x = 15, y = 5
cost of pen = Rs. 15
cost of pencil = Rs. 5
3. Let 20 paisa coins and 25 paisa coins be x and y respectively
Given
x + y = 50 ........(1)
0.20 x + 0.25 y = 11.50 ( multiply by 100 to remove decimals)
20 x + 25 y = 1150
4 x + 5 y = 230 ........(2)
0n solving (1) & (2)
x = 20 , y = 30
no, of 20 p coins = 20
no, of 25 p coins = 30
4. Let the two numbers be x and y respectively
Given
x + y = 137 .......(1)
x - y = 43 ,,,,,,,,(2)
on solving (1) & (2)
x = 90 , y = 47
The numbers are 90 and 47