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# ​maths king

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8

Lisa got an average score of 85 in 4 tests. She got 86 as the average of the highest 3 scores, and his lowest two scores are the same numbers. What is the average of her highest two scores?

# maths class 8

Balvinder writes down all the numbers from 1 to 3268 (including 1 and 3268). How many digits has he written down?

(1) If the volume of a cube is 8000 m3 , then what is the surface area of the cube?

(2) The length of a rectangle is increased by 60%. By what percentage should the width be reduced to keep the area of the rectangle the same?

(3) Solve the following using the standard identity (a+b) (a-b) = a 2 - b 2 A) 109 × 91 B) 1002 × 998 C) 103 × 97 D) 109 × 91

(4) The simple interest of Rs.6300 in 7 years at 8% per annum will be same as simple interest on Rs.16800 at 3% per annum in how many years?

(5) Sara and Iqbal run a hundred metres race. Sara wins by 20 metres. For the next race, Sara starts from 20 metres behind the original starting line, and Iqbal starts from the original starting line. If they both run at the same speed in which they ran the original race, who will win this race, and by how many metres?

(6) A garden is 300 metres wide and 400 metres long. There is a pathway that runs along the perimeter inside the garden. The area of the pathway is half of the area of the park. What is the  width of the pathway?

Sep 28, 2015

#8
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(6) A garden is 300 metres wide and 400 metres long. There is a pathway that runs along the perimeter inside the garden. The area of the pathway is half of the area of the park. What is the  width of the pathway?

Let x be the width of the pathway......then.....we have an inner rectangle whose area is defined as:

(300 - 2x) (400 - 2x)  = 60,000m^2  simplify

120000 - 1400x + 4x^2  = 60000   subtract 60000 from each side

4x^2 - 1400x  + 60000  = 0

x^2 - 350x + 15000  = 0 ........factor

(x - 50) (x - 300)  = 0  setting each factor to 0, x= 300m (reject) or x = 50m......which is correct   Sep 28, 2015

#1
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Balvinder writes down all the numbers from 1 to 3268 (including 1 and 3268). How many digits has he written down?

1 - 9  = 9 digits

10-99 = 180 digits

100-999 = 2700 digits

1000-3268 = 9076 digits

9 + 180 + 2700 + 9076  = 11965 digits   Sep 28, 2015
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Lisa got an average score of 85 in 4 tests. She got 86 as the average of the highest 3 scores, and his lowest two scores are the same numbers. What is the average of her highest two scores?

Lisa's scores are as follows: 89, 87, 82, 82=340

Her 4-tests average is: 340/4=85

89 + 87 +82=258/3=86 The average of the highest 3 scores.

89 + 87=176/2=88 The average of her highest two scores.

Sep 28, 2015
#3
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(4) The simple interest of Rs.6300 in 7 years at 8% per annum will be same as simple interest on Rs.16800 at 3% per annum in how many years?

The two investments should be equal in 7 years, where both investments will have earned the same amount of interest of 3,528 Rs.

Sep 28, 2015
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(2) The length of a rectangle is increased by 60%. By what percentage should the width be reduced to keep the area of the rectangle the same?

If the length of the rectangle is increased by 60%, then the width of the rectangle should be reduced by 37.5% in order to keep the area the same.

Sep 28, 2015
#5
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(5) Sara and Iqbal run a hundred metres race. Sara wins by 20 metres. For the next race, Sara starts from 20 metres behind the original starting line, and Iqbal starts from the original starting line. If they both run at the same speed in which they ran the original race, who will win this race, and by how many metres?

Assuming that the reach their top speeds instantaneously, for every meter that  Sara runs, Iqbal runs 4/5 of a meter

Then.......Sara will run 120m in the second race and Iqbal will run  (120)(4/5)m  = 96m....

Therefore.....Sara will win by 4 m   Sep 28, 2015
#6
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(1) If the volume of a cube is 8000 m^3 , then what is the surface area of the cube?

The side of the cube = (8003m^3)^(1/3)  = 29 m

The surface area is given by   6*(side)^2   =  6*(20m)^2 =  6 *400m^2  = 2400m^2   Sep 28, 2015
#7
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(3) Solve the following using the standard identity (a+b) (a-b) = a 2 - b 2 A) 109 × 91 B) 1002 × 998 C) 103 × 97 D) 109 × 91

B is the answer ......  a = 1000 and b = 2   Sep 28, 2015
#8
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(6) A garden is 300 metres wide and 400 metres long. There is a pathway that runs along the perimeter inside the garden. The area of the pathway is half of the area of the park. What is the  width of the pathway?

Let x be the width of the pathway......then.....we have an inner rectangle whose area is defined as:

(300 - 2x) (400 - 2x)  = 60,000m^2  simplify

120000 - 1400x + 4x^2  = 60000   subtract 60000 from each side

4x^2 - 1400x  + 60000  = 0

x^2 - 350x + 15000  = 0 ........factor

(x - 50) (x - 300)  = 0  setting each factor to 0, x= 300m (reject) or x = 50m......which is correct   CPhill Sep 28, 2015