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Question 1162243: Hello:
How do I setup and solve these inequalities?
1
Joe has $50 in his lunch account and spends $3 each day. Renee has $30 in her lunch account and spends $2 each day. After how many days will the balance in Joe’s account be more than the balance in Renee’s account.
2
Joe has $50 in his lunch account and spends $3 each day. Renee has $30 in her lunch account and spends $2 each day. After how many days will the balance in Joe’s account be less than the balance in Renee’s account?
Thanks in advance for your help.
Answer by ikleyn(52778)   (Show Source):
You can put this solution on YOUR website! .
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 (!)
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  from the COMPOUND inequalities
J(d) > R(d) AND d <= 15, when both functions J(d) and R(d) are defined and make sense.
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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
ANSWER. 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.
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
- Solving simple and simplest linear inequalities
in this site and learn the subject from there.
Consider this lesson as your textbook, guidebook, tutorials and (free of charge) home teacher.
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