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?

Question

priyansh2004 priyansh2004

15-06-2020
Mathematics

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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?

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Angel1126 Angel1126 · Answer 1 · 2020-06-15T18:17:50+02:00

Answer:

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: