math help plz

Question

Gabe Amodeo, a nuclear physicist, needs 90 liters of a 50% acid solution. He currently has a 30% solution and a 60% solution. How many liters of each does he need to make the needed 90 liters of 50% acid solution?
Gabe needs _________ liters of the 30% solution.

Answer 1

Allegation:

 

HAVE      WANT      NEED

30%........................10.....

..............50%..................

60%.......................20......

 

So you need 10 parts of 30% and 20 parts of 60% for a total of 30 parts

30 parts = 90 liters, thus 1 part = 3 liters

10 parts x 3 liters/part = 30 liters of 30% + 60 liters of 60%

 

Done another way:

x = L of 30%

y = L of 60%

x + y = 90

(x)(30) + (y)(60) = 90 x 50 = 4500

 

x = 90-y

(90-y)(30) + 60y = 4500

2700 - 30y + 60y = 4500

30y = 1800 

y = 60 liters of 60%

x = 30 liters of 30%