Question 7132
We start with 56 litres of pure pine juice. If they take out 8 litres, you'd then have 48 litres left. The mixture is still pure.


If it's refilled with 8 litres of mango juice, the resulting mixture will be 8 parts mango and 48 parts pine, or 1 part mango, 6 parts pine. (AKA, roughly 16.67% mango juice).


Now, if they take out 8 litres from that mixture, that 8 litres will also be 1 part mango and 6 parts pine, leaving you with 48 litres of 1 part mango, 6 parts pine.


Hang on, because it gets tricky from here. We're going to use a formula here:


{{{ q[1]p[1] + q[2]p[2] = (q[1]+q[2])p[3] }}} <---- where there are q[1] litres of p[1] % that we start with, and we add q[2] litres of p[2] % mix, and so we'll end up with a mixture that is (q[1] + q[2]) liters big that will have a different percent mixture p[3] from what we started.


We started with 48 liters that is 16.67% mango. So {{{ q[1]*p[1] = 48*0.1667 }}} <---- change the percent to a decimal.


We're going to add 8 liters of pure mango juice, so {{{ q[2]*p[2] = 8*1 }}} <--- The 100% mango juice is the 1 in decimal.


As total mix, we'll have {{{ q[1]+ q[2] }}} litres which is 48 + 8 = 56, BUT the percentage mango of the new mixture will surely be different.


So our equation so far is: {{{ 48*0.1667 + 8*1 = 56*p[3] }}}. All we have to do is solve for {{{p[3]}}}.


{{{  16 = 56p[3] }}} <---- simplified


{{{ p[3] = 0.2857142857 }}} <--- roughly 28.57% mango juice or {{{ 2/7 }}} mango juice. Since mango is 2/7 of the mixture, the other 5/7 is pine. The problem asked for the ratio between mango to pine, and that would be the 2:5.