How many tables should they plan to refinish?

​A furniture shop refinishes tables. Employees use two methods to refinish tables. Method I takes 0.5 hours and the material costs $8 . Method II takes 2.0 hours, and the material costs $6 . Next week, they plan to spend 94 hours in labor and $724 in material for refinishing tables. How many tables should they plan to refinish with each method? (Round to two decimal places if necessary.)

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x = number of tables refinished using method I
y = number of tables refinished using method II

Labor hours
0.5x + 2y = 94

Cost of materials
8x + 6y = 724

Solve the system:
0.5x + 2y = 94
8x + 6y = 724

0.5x + 2y = 94  {first equation}
0.5x = -2y + 94  {subtracted 2y from each side}
x = -4y + 188  {multiplied each side by 2}

Substitute -4y + 188, in for x, into second equation.

8x + 6y = 724  {second equation}
8(-4y + 188) + 6y = 724  {substituted}
-32y + 1504 + 6y = 724  {used distributive property}
-26y + 1504 = 724  {combined like terms}
-26y = -780  {subtracted 1504 from each side}
y = 30  {divided each side by -26}

Substitute 30, in for y, into x = -4y + 188.

x = -4y + 188
x = -4(30) + 188  {substituted}
x = -120 + 188  {multiplied}
x = 68  {added}

x = 68 and y = 30

They should plan on finishing:
68 tables using method I
​and 
30 tables using method II

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