Not understanding how to set up

Question

You need a 90% alcohol solution. On hand, you have a 25 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

Try alligation.  If you don't know what it is, you should google it.  It works pretty well.

 

HAVE..........WANT...........NEED

30%................................5 parts

....................90%....................

95%...............................60 parts

 

If 5 parts of 30% = 25 ml, then 60 parts = 12x that or 300 mls.  So, you need to add 300 mls of 95% to the 25 mls of the 30%.  This will give you 325 mls of 90%

Answer 2

let x=amount of the 95% mixture needed

30%(25)+95%(x)=90%(25+x)

0.3(25)+0.95(x)=0.9(25+x)

7.5+0.95x=22.5+0.9x

0.95x-0.9x=22.5-7.5

0.05x=15

5x=1500

x=1500/5

x=300 mL is needed of the 95% mixture

Answer 3

x represents the amount of 95%

0.30(25) + 0.95(x) = 0.90(25 + x)

 

Can you solve for x and answer?