How much 25% antifreeze and 50% antifreeze should be combined to give 40 gallons of 30% antifreeze?

Apr 12, 2017

32 gallons of 25% and 8 gallons of 50%

Explanation:

let a gallons of 25% antifreeze and b gallons of 50% antifreeze be needed to get 40 gallons of 30% antifreeze .
thus , $a + b = 40$
$30 = 25 \frac{a}{40} + 50 \frac{b}{40}$
$48 = a + 2 b$
now , $a = 40 - b$
$48 = 40 - b + 2 b$
therefore , $b = 8 g a l l o n s$
$a = 40 - 8 = 32 g a l l o n s$