SOLUTION: Three peaches and a banana cost 98 cents. Six peaches and a banana cost $1.79. How much does one banana cost?

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Question 1149492: Three peaches and a banana cost 98 cents.
Six peaches and a banana cost $1.79.
How much does one banana cost?
Answer by greenestamps(13206) About Me  (Show Source):
You can put this solution on YOUR website!


Using logical reasoning....

(1) Compare the two purchases to determine how much the additional three peaches cost.

(2) You know the cost of three peaches and one banana; use your answer from (1) to determine the cost of the banana.

Algebraically....
                 6p+1b = 179
                 3p+1b =  98
                 -----------
    difference:  3p    =  81

Then....

                3p+1b = 98
                3p    = 81
                ----------
   difference:     1b = 17

That solution using algebra is step for step the same as the preceding solution using logical reasoning.

Here is an alternative algebraic solution which probably isn't the way you would solve the problem using logical reasoning; but it makes the algebraic solution easier.

(1) Double the first purchase to get 6 peaches and 2 bananas for 2($0.98) = $1.96. Then compare the two purchases:
                 6p+2b = 196
                 6p+1b = 179
                 -----------
    difference:     1b =  17


That path to the solution gets you to the final answer in fewer steps.