% ?What number should be added to 6, 15, 20 and 43 to make the numbers

1.	% ?What number should be added to 6, 15, 20 and 43 to make the numbers anproportional.
Answer» Let us add, say x to all the four numbers, (6+x):(15+x) = (20+x):(43+x), or (6+x)(43+x) = (15+x)(20+x), or 258 + 49x + x^2 = 300 +35x + x^2, or 49x-35x = 14x = 300–258=42, or x = 3. So you need to add 3 to 6, 15, 20 and 43 to make them 9:18 ::23:46 which in the proportion of 1:2::1:2.

% ?What number should be added to 6, 15, 20 and 43 to make the numbers anproportional.

Answer»

Let us add, say x to all the four numbers,

(6+x):(15+x) = (20+x):(43+x), or

(6+x)(43+x) = (15+x)(20+x), or

258 + 49x + x^2 = 300 +35x + x^2, or

49x-35x = 14x = 300–258=42, or

x = 3.

So you need to add 3 to 6, 15, 20 and 43 to make them 9:18 ::23:46 which in the proportion of 1:2::1:2.