Question 1162243
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            This problem is  VERY  UNUSUAL  and  OUTSTANDING   (!)


            So,  read my solution  VERY  ATTENTIVELY   (!)


            I solved only first problem,  in order for you could concentrate/focus your attention   (!)



<pre>

Joe's balance after d days is  

    J(d) = 50 - 3d  dollars, under the condition d <= 16.


    Notice that at the 17-th day, Joe will not be able to spend 3 dollars for lunch (!)



Renee's balance after d days is

     R(d) = 30- 2d,  under the condition d <= 15.


     Notice that at the 16-th day, Renee will not be able to spend 2 dollars for lunch (!)



The problem asks to find the number of days  {{{highlight(highlight(d))}}}  from the COMPOUND inequalities

    J(d) > R(d)  AND  d <= 15,  when both functions J(d) and R(d) are defined and make sense.


    +---------------------------------+
    |   The setup is just completed.  |
    +---------------------------------+


Now you should solve this inequality  J(d) > R(d),  which is  50 - 3d > 30 - 2d.  


For it, collect the terms containing "d" on the right side; 
collect constant terms on the left side


    50 - 30 > 3d - 2d

    20      > d


which is the same as d < 20.


But the function R(d) is not defined after d = 15;  so the answer to the problem's question is


<U>ANSWER</U>.  During the entire time period  1 <= d <= 15, when Renee still has money to buy her lunch,
         Joe will have MORE money in his balance than Renee.
</pre>

Thus the first problem is just solved.


Try to solve the second problem by the same way.


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Solving inequalities is critically important skills for beginner student.


See the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Inequalities/Solving-simple-and-simplest-inequalities.lesson>Solving simple and simplest linear inequalities</A> 

in this site and learn the subject from there.


Consider this lesson as your textbook, &nbsp;guidebook, &nbsp;tutorials and &nbsp;(free of charge) &nbsp;home teacher.