mixture problems

Question

How much water should be added to 50 ml of 25% acid solution to dilute it to a 10% acid solution?

Answer 1

50 ml of 25% acid solution means 0.25*50=12.5 ml of acid and 50-12.5=37.5 ml of water

you want to add water to get a 10% acid solution which means you want the solution to be 90% water

(37.5+x)/(50+x)=90% where x=# of ml of water to add

(37.5+x)/(50+x)=9/10

cross multiply

10(37.5+x)=9(50+x)

375+10x=450+9x

10x-9x=450-375

x=75 ml of water to be added

check:(75+37.5)/(50+75)=112.5/125=225/250=9/10=90%, or...

12.5/125=125/1250=1/10=10%

Answer 2

75% (50) + 100%x = 90%(50 +x )

.75(50) + x = .9(50 + x)

37.5 + x = 45 + 0.9x

0.1x = 7.5

x = 75

 

75 ml must be added.