A chemical company makes two brands of antifreeze. The first brand is 20% pure antifreeze, and the second brand is 45% pure antifreeze. In order to obtain 30 gallons of a mixture that contains 30% pure antifreeze, how many gallons of each brand of antifreeze must be used?

First brand = 18 gallons

Second brand = 12 gallons

Step-by-step explanation:

Let the first brand brand be A and the second brand be B.

Thus, since he wants to obtain 30 gallons of a mixture that contains 30% pure antifreeze, then we have;

A + B = 30 - - - (eq 1)

Also; The first brand is 20% pure antifreeze, and the second brand is 45% pure antifreeze. Thus;

0.2A + 0.45B = (0.3 × 30)

0.2A + 0.45B = 9 - - - (eq 2)

From eq 1, we have; A = 30 - B

Put 30 - B for A in eq 2;

0.2(30 - B) + 0.45B = 9

6 - 0.2B + 0.45B = 9

0.25B = 9 - 6

0.25B = 3

B = 3/0.25

B = 12

Thus, A = 30 - 12 = 18 gallons

the radius is 2 times the diameter.

step-by-step explanation: