Question

What number must be added to each of the numbers 25, 33, 46, 60 so that the numbers are in proportion?​

Answer 1

Answer:

Given :

The numbers 25,33,46,60 .

To find -  The number that must be added to each of the numbers 25,33,46,60 so that the numbers are in proportion.

Solution -  We simply solve this mathematical problem by using the following mathematical process.

Let, the number added be = x

(25+x) : (33+x) : : (46+x) : (60+x)

=> (25+x) / (33+x) = (46+x) / (60+x)    

=>  (25+x) (60+x) = (46+x) (33+x)                            [cross multiplying]

=> 1500 + 25 x + 60 x +$x^{2}$ =1518 +46 x +33 x +$x^{2}$

=> 1500 +85 x + $x^{2}$ = 1518 + 79 x +$x^{2}$

=> 85 x -79 x = 1518 -1500

=> 6 x= 18

=> x = 3

Hence, the number that must be added to the numbers 25,33,46,60 to make the number proportional is 3.

Answer 2

Answer:

3 must be added to each of the given numbers so that they are in proportion.

Step-by-step explanation:

Let 'x' be added to each of the given number

Therefore the numbers become 25 + x , 33 + x , 46 + x , 60 + x

We know that for the numbers in proportion,

Product of means = Product of extremes

=> (33 + x)(46 + x) = (25 + x)(60 + x)

=> 1518 + 79x + x² = 1500 + 85x + x²

=> 1518 - 1500 = 85x - 79x

=> 18 = 6x

=> 3 = x

Therefore, 3 must be added to each of the given numbers so that they are in proportion.