Question

how much antifreeze 25% antifreeze and 50% antifreeze should be combined to give 40 gallon of 30% antifreeze?​

Answer 1

32 gallons of 25 % antifreeze should be combined with 8 gallons of 50 % antifreeze to get 40 gallon of 30% antifreeze

Solution:

From given,

Final mixture is 40 gallon

Let "x" be the gallon of 25 % antifreeze

Then, (40 - x) is the gallon of 50 % antifreeze

Therefore, according to question,

"x" gallons of 25 % antifreeze should be combined with (40 - x) gallons of 50 % antifreeze to get 40 gallon of 30% antifreeze

Therefore, we frame a equation as:

25 % of x + 50 % of (40 - x) = 30 % of 40

Solve for "x"

$\frac{25}{100} \times x + \frac{50}{100} \times (40-x) = \frac{30}{100} \times 40\\\\0.25x + 0.5(40-x) = 12\\\\0.25x + 20 - 0.5x = 12\\\\0.25x - 0.5x = 12 - 20\\\\-0.25x = -8\\\\0.25x = 8\\\\Divide\ both\ sides\ by\ 0.25\\\\x = 32$

Thus, 32 gallons of 25 % antifreeze is used

Then, (40 - x) = (40 - 32) = 8

Thus 8 gallons of 50 % antifreeze is used