Linear Equations Made Great : With Practice Worksheet For Class 5th,6th,7th[13]

1)A man is thrice as old as his son. Five years ago, the man was four times as old as his son. Find their present ages.

2) After 16 years, Fatima will be three times as old as she is now. Find her present age.

3) After 32 years, Rahim will 5 times as old as he was 8 years ago. How old is Rahim today ?

4) A bag contains 25-paisa and 50-paisa coins whose total value is Rs. 30. If the number of 25 paisa coins is four times that of 50 paisa coins, find the number of each type of coins.

5) Five times the price of a pen is Rs. 17 more than three times its price. Find the price of the pen.
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SOLUTION :
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1) Let the present age of the son = x years and the man’s present age = 3x years
Five years ago,
son’s age =( x – 5) years and man’s age = (3x -5) years
According to the question,
(3x – 5) = 4 ( x -5 )
3x – 5 = 4x – 20
3x – 4x = – 20 + 5
– x = – 15 x = 15
Thus, son’s present age = x =15 years and man’s present age = 3x = 3 * 15 = 45 years
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2) Let Fatima’s present age = x years
After 16 years, her age will be =(x + 16 )years
According to the question,
( x + 16 ) = 3 ( x )
x + 16 = 3x
16 = 3x – x
16 = 2x x = 16 / 2 x = 8
Hence, Fatima’s present age is 8 years.
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3) Age 8 years ago ______Present age _______Age after 32 years
( x – 8) years x years ( x + 32 ) years

Let Rahim’s present age be = x years
8 years ago his age = ( x – 8 ) years
After 32 years, his age will be = ( x + 32 ) years
According to the question,
( x + 32 ) = 5 ( x – 8 )
x + 32 = 5x – 40
32 + 40 = 5x – x
72 = 4x x = 72 / 4 x = 18
Thus , Rahim’s present age 18 years. ______________________________________________________________________________________________



4) Total value = Rs. 30 = 3000 paise
Let No. of 50 paise coins = x So, total amount of 50 paise = 50x paise
No. of 25 paise coins = 4x So, total amount of 25 paise = 25 * 4x = 100x paise.
According to the question,
50x + 100x = 3000
150x = 3000 x = 3000/150 x = 20

Number of 50 paise coins = x = 20 coins
Number of25 paise coins = 4x = 4* 20 = 80 coins
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5) Let the price of the pen be= Rs. x

According to the question,
5x = 3x + 17
5x – 3x = 17 2x =17 x = 17 / 2 x = 8.5
Thus, the price of the pen is Rs. 8.5
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1] KNOWING YOUR NUMBERS [1]