Question 801838
this will use 2 equations, solved using the addition method

x + y = 100
30x + 90y = 75

start by multiplying 100 x 75 and putting the answer in the bottom equation...

x + y = 100
30x + 90y = 7500

now, time to get rid of one of the variables, lets get rid of x by multiplying the top line by -30 and adding the two lines together...

-30x - 30y = -3000
30x + 90y  = 7500
...................
60y = 4500

divide both sides by 60

y = 75

now we know the value for y, lets plug that number into the original equation to find the value of x

30x + 90(75) = 7500

30x + 6750 = 7500

subtract 6750 from both sides

30x = 750

divide both sides by 30

x = 25

so now we know, 25 gallons of 30% solution and 75 gallons of 90% solution.