<h2>21.</h2>
Let x represent the original number of books (the value we're asked for by the problem question). Then after this number was doubled, its was 2x. After 4028 was added, it was 2x+4028. That value is given by the problem statement as being 51,514, so the equation can be ...
... 2x + 4,028 = 51,514
... 2x = 47,486 . . . . . . . . . . . subtract 4028
... x = 23,743 . . . . . . . . . . . . divide by 2
The library had 23,743 books before the transactions described.
<h2>22.</h2>
Let t represent the number of minutes required for you to finish. Then in t minutes, you have prepared 2t carrots. The number of carrots you need can be described by ...
... 2t + 18 = 60
... t + 9 = 30 . . . . . . divide by the coefficient of t
... t = 21 . . . . . . . . . . subtract 9
It will take you 21 minutes to finish.
<h2>23.</h2><h3>Given</h3>
- cost is $39.95 plus $0.35 for each minute over 500
<h3>Find</h3>
- cost as a function of the number of minutes usage over 500
- the number of minutes over 500 for a bill of $69.70
<h3>Solution</h3>
Let m represent the number of minutes usage over 500. Let c(m) represent the cost as a function of m. The given relation can be expressed as
... c(m) = 39.95 + 0.35m
We can substitute the bill information to find m:
... 69.70 = 39.95 + 0.35m
... 29.75 = 0.35m . . . . . . . . . subtract 39.95
... 85 = m . . . . . . . . . . . . . . . . divide by 0.35
The number of minutes over 500 for a bill of $69.70 is 85 minutes.
