Question

chemical company makes two brands of antifreeze. the first brand is 40% pure antifreeze, and the second brand is 70% pure antifreeze. in order to obtain 180 gallons of a mixture that contains 45% pure antifreeze, how many gallons of each brand of antifreeze must be used? first brand: gallons second brand: gallons

Explanation:

Step1: Let first brand be $x$ gallons, second be $180 - x$ gallons.

$0.4x+0.7(180 - x)=0.45\times180$

Step2: Expand and simplify.

$0.4x + 126-0.7x=81$
$-0.3x=81 - 126$
$-0.3x=-45$

Step3: Solve for $x$.

$x = 150$
Second brand is $180 - 150=30$ gallons.

Answer:

First brand: 150 gallons
Second brand: 30 gallons