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?

**x = number of tables with method 1**

y = number of tables with method 2

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}

———————-

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

70 tables using method 2

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