Furniture Shop - System of Equations

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 $10. Method II takes 2 hours, and the material costs $6. Next week, they plan to spend 175 hours in labor and $1120 in material for refinishing tables. How many tables should they plan to refinish with each method?

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

​0.5x + 2y = 175 {hours making each table}
10x + 6y = 1120 {cost making each table}

-1.5x - 6y = -525 {multiplied top equation by -3}
10x + 6y = 1120 {bottom equation stays the same}
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​8.5x = 595 {added the 2 equations}
x = 70 {divided each side by 8.5}

10x + 6y = 1120 {second equation from above}
10(70) + 6y = 1120 {substituted 70, in for x, into second equation}
700 + 6y = 1120 {multiplied 10 by 70}
6y = 420 {subtracted 700 from each side}
y = 70 {divided each side by 6}

70 tables using method 1
70 tables using method 2

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