Question 1199473
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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.<br>
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.<br>
On this problem I personally would probably go with a variation of the method from the third tutor, like this:<br>
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:<br>
{{{12*(286/260)=12*(11/10)=132/10=13.2}}}<br>