Question

what number should be subtracted from each of the numbers 18,31,23and 41,so that the new number are in proportion​

Answer 1

Answer:5

Step-by-step explanation:

Let the integer to be subtracted be ‘x’.

When we say that 18, 31, 23 and 41 are to be brought to proportion by subtracting the same number from them, we can just say that the numbers in proportion after the operation shall be :

(18−x):(31−x)::(23−x):(41−x)  

or,  (18−x)/(31−x)=(23−x)/(41−x)  

or,  (18−x)(41−x)=(23−x)(31−x)  (cross-multiplication)

or,  18(41−x)−x(41−x)=23(31−x)−x(31−x)  

or,  738−18x−41x+x2=713−23x−31x+x2  

or,  738−59x=713−54x  

(subtracting ‘ x2 ’ on both sides along with solving further.

or,  −59x+54x=713−738  

(adding ‘ 54x ’ and subtracting ‘738′ on both sides.)

or,  −5x=−25  

or,  x=5  (dividing ‘ −5x ’ on both sides.)

Thus, the number to be subtracted from each terms (number) is 5