Question 1184038
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NOTE: The other tutor interpreted the phrase "the second jug had twice the volume of diluted cordial compared to the first" to mean the amount of ACTUAL cordial in the two jugs was in the ratio 1:2.  That is a possible interpretation; my solution below interprets that phrase to mean the amount of DILUTED CORDIAL -- i.e., the total amounts of mixture in the two jugs -- was in the ratio 1:2.<br>
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A 2:5 ratio of cordial to water in the first jug means 2/7 of that diluted cordial is cordial; a 3:7 ratio in the second jug means 3/10 of that diluted cordial is cordial.<br>
The volume of the diluted cordial in the second jug is twice the volume of the diluted cordial in the first, so when the contents are combined 2/3 of the mixture is from the second jug.  The fraction of cordial in the final mixture is then<br>
{{{(2/3)(3/10)+(1/3)(2/7) = 1/5+2/21 = 21/105+10/105 = 31/105}}}<br>
The ratio of cordial to water in the mixture is then 31:(105-31) = 31:74.<br>
ANSWER: 31:74<br>