A furniture shop refinishes tables. Employees use one of two methods to refinish each table. Method I takes 1.5 hours and the material costs $10. Method II takes 2.5 hours, and the material costs $5. Next week, they plan to spend 308 hours in labor and $1260 in material for refinishing tables. How many tables should they plan to refinish with each method?

Question

Mathematics

Jaydin Burke

5 March, 17:58

A furniture shop refinishes tables. Employees use one of two methods to refinish each table. Method I takes 1.5 hours and the material costs $10. Method II takes 2.5 hours, and the material costs $5. Next week, they plan to spend 308 hours in labor and $1260 in material for refinishing tables. How many tables should they plan to refinish with each method?

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Answers (1)

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Zechariah · Answer 1

Let X be the number of method I tables, Y method II tables.

1.5x+2.5y=308. Hours spent

10x+5y=1260. Cost

Multiply the equation 1 by 2

3x+5y=616

10x+5y=1260

Subtract the equation 1 from the equation 2 to get

7x=644

X=644:7

X=92. number of method I tables

So then

10 (92) + 5y=1260

920+5y=1260

5y=1260-920

5y=1,260-920

5y=340

Y=340:5

Y=68 number of method II tables