A chemical company makes two brands of antifreeze. The first brand is 85% pure antifreeze, and the second brand is 90% pure antifreeze. In order to obtain 50 gallons of a mixture that contains 50% pure antifreeze, how many gallons of EACH brand of antifreeze must be used?

Let +a+ = gallons of 55% antifreeze needed

Let +b+ = gallons of 95% antifreeze needed

(1) +a+%2B+b+=+160+

(2) +%28+.55a+%2B+.95b+%29+%2F+160+=+.85+

(2) +.55a+%2B+.95b+=+.85%2A160+

(2) +.55a+%2B+.95b+=+136+

(2) +55a+%2B+95b+=+13600+

(2) +11a+%2B+19b+=+2720+

Multiply both sides of (1) by +11+

and subtract (1) from (2)

(2) +11a+%2B+19b+=+2720+

(1) +-11a+-+11b+=+-1760+

+8b+=+960+

+b+=+120+

and

(1) +a+%2B+120+=+160+

(1) +a+=+40+

40 gallons of 55% antifreeze are needed

120 gallons of 95% antifreeze are needed

check:

(2) +%28+.55a+%2B+.95b+%29+%2F+160+=+.85+

(2) +%28+.55%2A40+%2B+.95%2A120+%29+%2F+160+=+.85+

(2) +%28+22+%2B+114+%29+%2F+160+=+.85+

(2) +136+=+.85%2A160+

(2) +136+=+136+

OK

Step-by-step explanation:

goog may be able to you find that answer

the answer is 62.8 cubic units