SOLUTION: Frank drove 260 miles using 12 gallons of gas. At this rate, how many gallons of gas would he need to drive 286 miles?

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): You can put this solution on YOUR website!
Setup this SIMPLE proportion. OR, treat this as units conversion.

Doing as units conversion,

You finish this.
Answer by ikleyn(52767)   (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).

================

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): You can put this solution on YOUR website!

The purpose of this site is to help the student. It is not to show what clever mathematicians we tutors are. We should contemplate what the student is probably being taught in class. I think the method which josgarithmetic first suggested, SIMPLE PROPORTION, is what this student is studying in class. "Miles IS TO gallons AS Miles IS TO gallons": Cross multiply and solve for x. Edwin

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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