DAY 10

Comment

It is perhaps tempting to say that the mixtures taste the same, because the second mixture could be made by simply adding1 part juice and 1 part water to the first mixture.
On the other hand, 1 part juice and 1 part water des not taste the same as 8 parts juice and only 3 parts water ... .

Answer

The first mixture (8 parts orange juice with 3 parts water) is stronger.

Readers' methods

G Samson, Camberwell SE5:
the first mixture has two and two thirds times as much juice as water;
the second mixture has only two and a quarter times as much.

Meryl L, Wimborne BH22:
Sample 1: orange : water is 2.6 (recurring) : 1
Sample 2: orange : water is 2.25 : 1.
So sample 1 has more orange to one part of water than sample 2.

Caroline P, Wroughton SN4:
Find lowest common denominator for water (12).
Use to find ratio of orange : water for each mix:
8 : 3 becomes 32 : 12
9 : 4 becomes 27 : 12.
Therefore 8 orange: 3 water mix is stronger.

Paul K, Wimbledon SW19:
Orange fraction in each:
1. 8/(8+3) = 8/11 = 8*13 / 11*13 = 104/143
2. 9/(9+4) = 9/13 = 9*11 / 13*11 = 99/143
So more orange in 1st sample.