; CS101, Spring 2013
; HW 1 
; Writing expressions. 

; This file is intended to be opened within the DrRacket
; programming environment.  It contains meta-data that is
; unreadable in browsers, word processors and text editors.

; Once this file is open within DrRacket:
;
; UNDER Language MENU, SELECT:
;   Choose Language... Advanced Student
;   Press the Run icon


(display "\n         CS101 Assignment 1, Spring 2013")
(display "\n                 SOLUTIONS\n\n")

; Try pressing the Run button at the top right of the screen
; and check out what prints in the interactions window.   

; PLEASE READ CAREFULLY AND SAVE OFTEN (Save button top left,
; only appears if you make changes)! Make sure none of your lines
; extend past column 80.
;

(display "Problem 1. Writing algebraic Racket expressions. \n\n")
; 
;  Convert each of the following algebraic formulas to an   
;  equivalent Racket function call. Use the normal math
;  precedence rules when writing these expressions.
;  
;  Example 1:  4 - 5 * 2 would be written (- 4 (* 5 2))
;  
;  Show the expression followed by its resultant output. 
;  
;  For the expression given in Example 1, you would type 
;  the expression shown below in the definitions window 
;  and then press Run:
;  
;  (printf "4 - 5 * 2 = (- 4 (* 5 2)) ==> ~a~%" 
;          (- 4 (* 5 2))) 
;  
;  This will display the given string followed by an arrow
;  and then the result of evaluating the expression.
;  
;  a. 7 + 30 * 4
;  
;  b. 20 * 8 - 5
;  
;  c. (1 + 5) * 6 - 12/3
;  
;  Be sure to write the printf statements so that 1 blank line 
;  vertically separates each printf expression. You can use 
;  the (newline) function call OR embedded ~%s.
;  
;  INFORMATION: the printf function is like the display 
;  function, in that it causes its string argument to print 
;  in the interactions window. But the printf can also embed
;  the string representation of evaluated expressions inside
;  its string argument. The ~a says, "insert value here", and
;  the evaluated result of the expression (- 4 (* 5 2)) is 
;  converted to a string and inserted in place of the ~a.
;  The ~% causes a newline character to be printed.
;  
;  The printf statements for parts a-c are started for you,
;  just uncomment them and fill in the missing parts. 
;  


(printf "Example: 4 - 5 * 2 = (- 4 (* 5 2)) ==> ~a~%~%" 
        (- 4 (* 5 2))) 
(newline)
(newline)
(printf "a. 7 + 30 * 4 = (+ 7 (* 30 4)) ==> ~a~%~%" 
        (+ 7 (* 30 4)))
(newline)
(printf "b. 20 * 8 - 5 = (- (* 20 8) 5) ==> ~a~%~%" 
        (- (* 20 8) 5))
(newline)
(printf "c. (1 + 5) * 6 - 12/3 = (- (* (+ 1 5) 6) (/ 12 3)) ==> ~a~%~%" 
        (- (* (+ 1 5) 6) (/ 12 3))) 

(newline)
(newline)

(display "Problem 2. Write an arithmetic expression to calculate John's
           income tax.\n\n")
; 
;  The government computes income tax as 17% of a taxpayer's income after 
;  deducting $6000.  John worked at two jobs last year, earning $24718 at
;  the first and $14284 at the second.  Write a Racket algebraic expression 
;  to calculate John's income tax. 
;  
;  It's OK if the final expression is a fraction.  You can change the 
;  language to "Full Swindle" and run the program to see it as a decimal 
;  number (just change it back to "Advanced Student" afterward).
;  


(printf "John's income tax = (* (- (+ 24718 14284) 6000) .17) ==> ~a~%~%"
        (exact->inexact (* (- (+ 24718.0 14284.0) 6000.0) .17)))


(newline)
(newline)

(display "Problem 3. Write an arithmetic expression for a carpet seller.\n\n")
; 
;  A carpet store computes the cost of installing wall-to-wall carpet in 
;  a rectangular room by multiplying the length and width of the room (in 
;  feet) by the cost of carpet in dollars per square foot, and adding a 
;  flat $50 service charge.
;  
;  Write this expression for a room of length 25, width 20 and a carpet 
;  cost of $1.75/sq ft. Embed this expression in a print statement as you
;  did for problems 1 and 2.  There is no need to have 2 decimals after 
;  the dollar amount.
;  
 

(printf "The cost of carpet = (+ (* 25 20 1.75) 50) ==> $~a~%~%"
        (+ (* 25 20 1.75) 50))

(newline)
(newline)

(display "Problem 4. Write an arithmetic expression to compute a grade.\n\n")
; 
;  A student writes two midterm exams and a final exam. Suppose the two 
;  midterms are each worth 25% of the grade and the final exam is worth   
;  50%. 
;  
;  Write an expression to calculate the final grade for a student who
;  got an 85/100 on midterm 1, a 90/100 on midterm 2, and a 95/100 on 
;  the final. 
;  
;  It's OK if the final expression is a fraction. You can change the
;  language to "Full Swindle" to see it as a decimal number (just change 
;  it back to "Advanced Student" afterward).
;  


(printf 
 "The final grade = (+ (* 50 (/ (+ 85 90) 200) (* 50 (/ 95 100)) ==> ~a"
 (exact->inexact (+ (* 50.0 (/ (+ 85 90) 200.0)) (* 50.0 (/ 95 100.0)))))