math help plz

Question

A 30% solution of fertilizer is to be mixed with a 70% solution of fertilizer in order to get 160 gallons of a 60% solution. How many gallons of the 30% solution and 70% solution should be mixed?

How many gallons of the 30% solution should be mixed?
_____________gallons

Answer 1

Allegation

 

HAVE      WANT      NEED

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

...............60%......................

70%.........................30.........

 

So you need 10 parts of 30% and 30 parts of 70% (total 40 parts)

40 parts = 160 gallons, so 1 part = 4 gallons

10 parts of 30% = 10 x 4 gallons = 40 gallons of 30%

30 parts of 70% = 30 x 4 gallons = 120 gallons of 70%

 

 

 

Done another way: (x gal)(30%) + (y gal)(70%) = (160 gal)(60%) 30x + 70y = 9600 x + y = 160 gal x = 160 - y 30(160-y) + 70y = 9600 4800 - 30y + 70y = 9600 40y = 4800 y = 120 gallons of 70% x = 160 - 120 = 40 gallons of 30%