ratio problem solving

Question

2 unequal jugs are filled with diluted cordial with different concentrations. The first jug has cordial and water in the ratio of 2:5 and the 2nd jug has cordial and water ratio of 3:7. The contents of the two jugs are then combined. If the second jug has twice the volume of diluted cordial compared to the first what is the ratio of cordial to water in the final mixture?

The initial working out is:

Final mixture: 1:2 = 7:14 = 70:140.

I don't understand the above step in solving this problem Thanks.

Answer 1

2:5 means 2 cordial:5 water, which means 2/(2+5) = 2/7 = about 28.6% cordial

3:7 means 3/(3+7) = 3/10 =30% with twice the volume

mix them, weighted average = closer to 30 than to 28.6 = about 29.5% ratio

about 29.5/70.5= roughly 3:7, slightly less though than the 2nd jug's ratio.

take the weighted average, and weight the 2nd jug with 2 and 1st with 1, then divide by 3

(2/7+3/10+3/10)/3 = (2/7+6/10)/3 = (20/70 + 42/70)/3 = 62/70/3 = 31/35/3 = 31/105=29.52%

which is a ratio of 31/(105-31)

= exactly 31:74 ratio for the mixture

which is between 2:5 and 3:7, but closer to 3:7

1:2 can't be right. that would mean 1/3 = 33 1/3 % cordial

and both jugs are less than that.

mix two different solutions you get an average inbetween the two, not more than both, or less than both