Linear Equation Made Great : With Practice Worksheets For Class 5th,6th,7th[12]

Q.1 ) The number of boys in a school is 334 more than the number of girls. If the total strength of the school is 572. Find the number of girls in the school.

SOLUTION :
Let the number of girls be = x Hence, the number of boys =( x + 334)
According to the question,
x + ( x + 334 ) = 572
x + x + 334 = 572
2x = 572 – 334
2x = 238
x = 238 / 2 x = 119
Thus, the number of girls in the school is 119
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Q.2) The length of a rectangular hall is 5 meters more than its breadth. If the perimeterof the hall is 74 meters. Find its length and breadth.

SOLUTION:
Let the breadth of the rectangular hall be = x meters
and the length = ( x + 5 ) meters
Perimeter = 74 meters
According to the question,
Perimeter = 2 ( L + B )
74 = 2 ( x + 5 + x )
74 = 2 ( 2x + 5 )
74 = 4x + 10
74 – 10 = 4x
64 = 4x 64 / 4 = x 16 = x

Thus, the breadth = x =16 meters and the length = ( x + 5 ) = 16 + 5 = 21 meters
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Q.3)The length of the rectangular park is thrice it’s breadth. If the perimeter of the park is 168 meters, find it’s dimensions.

SOLUTION:
Let the breadth of the rectangular park = x meters and the length = 3x meters
Perimeter = 168 meters
According to the question,
Perimeter = 2 ( L + B )
168 = 2 ( 3x + x )
168 = 6x + 2x
168 = 8x x = 168 / 8 x = 21 meters
Thus, the breadth = x = 21 meters and the length = 3x = 3 * 21 = 63 meters
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Q.4) A wire of length 86 cm is bent in the form of a rectangle such that its length is 7 cm more than it’s breadth. Find the length and the breadth of the rectangle so formed.

SOLUTION:
Let the breadth of the rectangle be = x cm.
and the length = ( x + 7 ) cm.
Perimeter of the rectangle = length of the wire = 86 cm.
According to the question,
P = 2 ( L + B )
86 = 2 ( x + 7 + x )
86 = 2x + 14 + 2x
86 – 14 = 4x 72 = 4x 72 / 4 = x x = 18
Thus, the breadth of the rectangle = x = 18 cm and the length = x + 7 = 18 + 7 = 25 cm.
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Q.5) Mona ‘s father us thrice as old as Mona. After 12 years, his age will be twice that of his daughter. Find their present ages.

SOLUTION:
Let Mona’s present age be = x years and her father’s present age = 3x years
After 12 years,
Mona’s age = ( x + 12 ) years Her father’s age = ( 3x + 12 ) years
According to the question,
3x + 12 = 2 ( x + 12 )
3x + 12 = 2x = 24
3x – 2x = 24 – 12
x = 12
Thus, Mona’s present age = 12 years and her father’s present age = 3x = 3 * 12 = 36 years
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Q.6) If 5 is subtracted from three times a number , the result is 16. Find the number.

SOLUTION :
Let the required number be = x
According to the question,
3x – 5 = 16
3x = 16 + 5 3x = 21 x = 21 /3 x = 7
Hence, the required number is 7
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Q.7) Find the two numbers such that one of them exceeds the other by 9 and their sum is 81.

SOLUTION:
Let the smaller number be = x then the other number = ( x + 9 )
the sum of the two numbers = 81
According to the question,
x + ( x + 9 ) = 81
x + x + 9 =81
2x = 81 – 9
2x = 72 x = 72 /2 x = 36
Thus, one number is 36 and the other number is x + 9 = 36 + 9 = 45
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PRACTICE WORKSHEETS { FREE DOWNLOAD } :-

1] KNOWING YOUR NUMBERS [1]