Kindly asking for help. Antifreeze math problem.

Question

a chemical company makes two brands of antifreeze. the first brand is 40 pure antifreeze, and the second brand is 65% pure antifreeze. in order to obtain 120 gallons of a mixture that contains 60% pure antifreeze, how many gallons of each brand of antifreeze must be used?

Answer 1

65x +40(120-x)= 60(120)

65x-40x = (60-40)(120)

25x = 20(120)

x =20(120)/25= 4(120)/5 = 4(24) = 96 gallons 65%

mixed with

24 gallons 40^%

to get

120 gallons 60%

65-60=5

60-40=20

20/5 = 4

96/24 = 4