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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.

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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