Question

Really starting to dislike this site.. Asked this three times and can't understand it.. salesperson purchased a car 27 mi/gal city 38 mi/gal highway. Recent trip 1654 miles. Required 47 gallons. How many miles driven in city

Answer 1

Here I'll help you better understand your problem :)

Answer 2

thanks :)

Answer 3

Is this the problem you mentioned in your message to me?

Answer 4

yeah i have several others but this is one

Answer 5

What is the required 47 gallons part?

Answer 6

how many gallons it took for the trip

Answer 7

Brit: I'll be right with you.

Answer 8

i got to go get ready for work leave me a message and il check it later

Answer 9

All right. I've solved the problem. You message me, please, when you're available to discuss this problem further.

Answer 10

Looks like several helpers are offering you suggestions! I'll leave it to you, Brit, whether or not to contact me again to discuss this problem. Have a good day!

Answer 11

c + h = 47 --->h = 47 - c
27c + 38h = 1654
now sub 47 - c in for h in the 2nd equation
27c + 38(47 - c) = 1654
27c + 1786 - 38c = 1654
- 11c = 1654 - 1786
-11c = - 132
c = 132/11
c = 12
now sub 12 in for c
c + h = 47
12 + h = 47
h = 47 - 12
h = 35
check...
27c + 38h = 1654
27(12) + 38(35) = 1654
324 + 1330 = 1654
1654 = 1654 (correct)

12 city miles were driven

Answer 12

Drove 1654 miles using 47 gallons of gasoline. Highway miles are 38 to the gallon, city miles are 27 to the gallon.

You can think of this problem in terms of how many gallons of gas are used in each sort of driving, and then find the miles from that at the end.

Let's let \(x\) be the number of gallons used for city driving. Then \(47-x\) is the number of gallons used for highway driving.

27x = number of miles driven in the city
38(47-x) = number of miles driven on highway
27x+38(47-x) = 1654 total miles driven = city + highway

\[27x + 38*47-38x = 1654\]Solve that for \(x\), and multiply \(x\) by 27 to get city miles.

Answer 13

crap....I messed up
I found gallons instead of miles.
So, whpalmer, would you multiply 12 x 27 to get the city miles ?

Answer 14

Exactly!

Answer 15

I kinda went about finding the answer the long way

Answer 16

TC: Appreciate your checking your own work and your honesty in admitting that your results were incorrect. Bet you can solve this problem!

Answer 17

12*27 = 324 city miles
(47-12)*38 = 1330 highway miles
total = 1330+324 = 1654

Answer 18

you guys are so smart....glad you were here to find my mistake. THX

Answer 19

@whpalmer4: Congrats. Your presentation is clear and accurate. My own work confirms the correctness of yours.

Answer 20

You can write the equations to do it directly in miles, but then you end up having to do fractions:

If we let \(c\) be city miles, then we use \(\frac{c}{27}\) gallons of gas on the city miles. Similarly, if \(h\) is highway miles, we use \(\frac{h}{38}\) gallons on the highway.

\[\frac{c}{27} + \frac{h}{38} = 47\](total gallons used)
\[c+h=1654\]Now solve by substitution, and get respective mileage quantities directly.