Question 1199473: Frank drove 260 miles using 12 gallons of gas. At this rate, how many gallons of gas would he need to drive 286 miles?
Found 4 solutions by josgarithmetic, ikleyn, Edwin McCravy, greenestamps:
Answer by josgarithmetic(39615)   (Show Source):
Answer by ikleyn(52765)  (Show Source):
You can put this solution on YOUR website! .
We see that 286 = 260 + 26 = 260 + 0.1*260 miles.
Therefore, the number of gallons needed is 12 + 0.1*12 = 12 + 1.2 = 13.2 gallons. ANSWER
Solved (mentally).
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Edwin, it did not go out of my attention on how you try to criticize my approach.
But my goal is not always to follow the teachers in their classrooms.
Very often my goal is to wake up the student's brain/mind from hibernation.
Sometimes, it is much more important deal than follow the standard rules.
Answer by Edwin McCravy(20054)  (Show Source):
Answer by greenestamps(13198)  (Show Source):
You can put this solution on YOUR website!
Regarding the comments on other responses to your post, I would very definitely go with tutor @ikleyn rather than tutor @Edwin. I find it is often far better to show students easy ways to solve problems using logical reasoning and simple arithmetic, rather than trying to guess how the student is being taught to solve the problem in class.
I remember when I was in elementary school in the 1950s the way to teach solving proportions was "the product of the means is equal to the product of the extremes". I was very relieved to discover that solving proportions was much easier than trying to figure out what that meant.
On this problem I personally would probably go with a variation of the method from the third tutor, like this:
The distance changes from 260 miles to 286 miles, so to find the number of gallons of gas needed fro 286 miles, you multiply the number of gallons required for 260 miles by the ratio of increase, 286/260:
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