# I am not understanding the exercise so I am feeling generous and giving loads of points (20). 1. Twenty-three times a certain number is much above 14 as 16 is above seven times the number: find it. 2. Divide 105 in two parts, one of which diminished by 20 shall be equal to the other diminished by 15. 3. Find 3 consecutive numbers whose sum is equal to 84. 4. The sum of two numbers is 8, and one of them with 22 added to it is five times the other; find the numbers. 5. The difference between the squares of two consecutive numbers is 121: find the numbers.

1
by Opubose

2014-11-27T16:32:39+05:30

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1) Let the number be x

so  according to question 23x - 14 = 16 - 7x
⇒ 30x = 30
⇒ x = 1

2) let the one half be x and so other is 105 - x

so according to question  x - 20 = 105 - x - 15

⇒ 2x = 110
⇒ x = 55

so the no is divided into 55 and 105 - 55 = 50

3) Let the three consecutive numbers be x - 1 , x  , x + 1

so according to question x - 1 + x + x + 1 = 84

⇒3x = 84 ⇒ x = 28

so the numbers are 27,28, 29

4) Let the two numbers be x,y

so x + y = 8 ... (i)

and x + 22 = 5y ⇒ 5y - x = 22 ... (ii)

x + y + 5y - x = 22 + 8
⇒ 6y = 30
⇒ y = 5

x = 8 - 5 = 3

so the two numbers are 3 and 5

5) let the two consecutive numbers be x, x + 1

so according to question (x + 1)² -  x² = 121

⇒ x² + 2x + 1 -  x² = 121
⇒ 2x = 120 ⇒ x = 60

so the numbers are 60,61
hope it helps
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