A word problem for my college algebra class

Question

A lamp manufacturing company produces 1600 reading lamps a day when it operates in two shifts. The first shift produces only 5/6 as many lamps as the second shift. Let x = the number of lamps produced per day by second shift. Write an algebraic expression in x for the number of lamps produced per day by the first shift. 

Answer 1

During the second shift, x lamps are produced. During the first shift, (5/6)x lamps are produced. During both shifts, 1600 lamps are produced. If we restate this information as an algebra equation, we get the following equation:

• first shift lamps PLUS second shift lamps EQUALS 1600 lamps : (original problem)
• (5/6)x + x = 1600 : (restated as an equation)
• (5/6)x + (6/6)x = 1600 : (add the (6/6) term to x in order to make all x terms sixths, since six sixths equals one)
• (11/6)x = 1600 : (five sixths plus six sixths is eleven sixths)
• (11/6)x * (6/11) = 1600 * (6/11) : (multiply both sides by (6/11))
• x = 1600 * (6/11) : (simplify the left side)
• x = 872.72727 : (simplify the right side)

Answer 2

"Write an algebraic expression in x for the number of lamps produced per day by the first shift"

 

Number for first shift + Number for second shift = Total number per day

 

(5/6)(Number for second shift) + (Number for second shift) = 1600        [givens]

(5/6)x                                     + x = 1600                                          [given]

 

    (5/6)x + x = 1600   [note: these are algebraic expressions in x]

       (11/6)x = 1600

            x = 873 [note that rounding is essential to make sense of this problem]

 

   Check:     Does (5/6)873 + 873 = 1600   ?

                              727  + 873  = 1600   ?

                                    1600 = 1600   ?yes