Question 1149492
<br>
Using logical reasoning....<br>
(1) Compare the two purchases to determine how much the additional three peaches cost.<br>
(2) You know the cost of three peaches and one banana; use your answer from (1) to determine the cost of the banana.<br>
Algebraically....<br><pre>
                 6p+1b = 179
                 3p+1b =  98
                 -----------
    difference:  3p    =  81

Then....

                3p+1b = 98
                3p    = 81
                ----------
   difference:     1b = 17</pre>
That solution using algebra is step for step the same as the preceding solution using logical reasoning.<br>
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.<br>
(1) Double the first purchase to get 6 peaches and 2 bananas for 2($0.98) = $1.96.  Then compare the two purchases:<br><pre>
                 6p+2b = 196
                 6p+1b = 179
                 -----------
    difference:     1b =  17</pre><br>
That path to the solution gets you to the final answer in fewer steps.<br>