PreCalculus 12thgrade

Question

You need a 35% alcohol solution. On hand, you have a 600 mL of a 30% alcohol mixture. You also have 95% alcohol mixture. How much of the 95% mixture will you need to add to obtain the desired solution?

Answer 1

let x=the number of ml of the 95% solution that is needed

30%(600)+95%(x)=35%(600+x)

0.3(600)+0.95x=0.35(600+x)

180+0.95x=210+0.35x

0.95x-0.35x=210-180

0.6x=30

6x=300

x=300/6

x=50 ml of the 95%solution is needed

check: 30%(600)=180ml and 95%(50)=47.5ml

180+47.5=227.5 ml of alcohol out of a total of 650 ml

227.5/650=2275/6500=91/260=7/20=35/100=35% or...

35%(650)=227.5