The frist brand is 30% and the second on is 55% in order to obtain 30 gallons of mixture that contains 35% how many gallons of each brand must you usr

yeet

first brand quantity is x

2nd brand quantity is y

x+y=30

0.3x+0.55y=0.35 (30) or 0.3x+0.55y=10.5

solve for x and y

multiply first equation by - 0.3

-0.3x-0.3y=-9

add to 2nd equation

0.3x-0.3y=-9

0.3x+0.55y=10.5 +

0x+0.25y=1.5

0.25y=1.5

divide both sides by 0.25

y=6

sub back

x+y=30

x+6=30

x=24

you need 24 gallons of the first brand and 6 gallons of the 2nd brand

Answer: First Brand = 24 gallons, Second Brand = 6 gallons

Explanation:

Quantity % Qty (%)

First Brand x 0.30 0.30x

Second Brand 30 - x 0.55 0.55 (30 - x) = 16.5 - 0.55x

Total 30 * 0.35 = 0.30x + 16.5 - 0.55x

30 (0.35) = 16.5 - 0.25x

10.5 = 16.5 - 0.25x

-6.0 = - 0.25x

24 = x

Second Brand: 30 - x = 30 - 24 = 6