Preston antifreeze is 20 antifreeze and Icefree is 12 antifr

Preston antifreeze is 20% antifreeze and Icefree is 12% antifreeze. How much of each should be used to get a 22 quart mixture of 15% antifreeze?
Thanks in advance

Solution

total qty.of mixture =22 quarts
let preston in the mix =x quarts
so icefree in the mix =22-x quarts
Preston antifreeze is 20% antifreeze ..so x quarts would have x*20/100=x/5 quarts..anti freeze
Icefree is 12% antifreeze..so 22-x quarts would have (22-x)*12/100=3(22-x)/25
=(66-3x)/25 quarts..antifreeze..
so total antifreeze in the mix =x/5+(66-3x)/25...
but the final mix had 15% antifreeze..in 22 quarts total antifreeze is =22*15/100=33/10...hence we have
x/5+(66-3x)/25=33/10
((5x+66-3x)/25)=33/10
(2x+66)/25=33/10
2x+66=33*25/10=165/2
2x=165/2-66=(165-2*66)/2=(165-132)/2=33/2...
x=33/(2*2)=33/4 = 8.25 quarts of preston and
22-x=22-8.25=13.75 quarts of icefree