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on a trip jennifer noticed that her car averaged 21 mi/gal of gas except
for the days she used the air conditioning, and then it averaged only 17 mi/gal.
if she use 91 gal of gas to drive 1751 mi, on how many of those miles
did she used the air conditioning?
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Let x be the miles where she used the air conditioning.
Then miles where she didn't use the air conditioning were (1751-x).
Now we can write this equation for the total gas spent
+ = 91 gallons of gas (total). (*)
+------------------------------------------------+
| At this point, the setup is just complete, |
| and our task is to solve this equation. |
+------------------------------------------------+
For it, multiply both sides by 21*17. You will get
17x + 21*(1751-x) = 91*21*17
17x + 21*1751 - 21x = 32487
17x - 21x = 32487 - 21*1751
-4x = -4284
x = = 1071.
ANSWER. She used the air conditioning on 1071 miles.
CHECK. I will check if equation (*) is held.
+ = 51 + 40 = 91 gallon of gas, in total. ! Correct !
Solved.