methods/algebra

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methods/algebra

A furniture shop refinishes tables.  Employees use one of two methods to refinish each table.  Method I takes 0.5 hours and the material costs $9.  Method II takes 2 hours, and the material costs $6.  Next week, they plan to spend 199 hours in labor and $1302 in material for refinishing tables.  How many tables should they plan to refinish with each method?
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Re: methods/algebra

x = number of tables with method 1
y = number of tables with method 2

0.5x + 2y = 199   {TIME}  -----> -1.5x - 6y = -597   {multiplied top equation by -3}
9x + 6y = 1302   {COST} ------>     9x + 6y = 1302   {bottom equation stays the same}
                                                   -------------------
                                                    7.5x = 705   {added the two equations}
                                                            x = 94   {divided by 7.5}

9x + 6y = 1302   {bottom original equation}
9(94) + 6y = 1302   {substituted 94, in for x, into bottom original equation}
846 + 6y = 1302   {multiplied}
6y = 456   {subtracted 846 from each side}
y = 76   {divided by 6}

94 tables with method 1
76 tables with method 2


@AlgebraHouse