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

Answers

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

This Is a Certified Answer

×
Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
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) 

so adding (i) and (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
1 5 1