i need some major help figuring this out

Mathematics
Tutor: None Selected Time limit: 1 Day

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
$9
. Method II takes
2.5
hours, and the material costs
$4
. Next week, they plan to spend
181
hours in labor and
$580
in material for refinishing tables. How many tables should they plan to refinish with each method?
Sep 28th, 2015

Thank you for the opportunity to help you with your question!

The question is not clear but after copy and paste you get the values:

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
$9. Method II takes
2.5 hours, and the material costs
$4. Next week, they plan to spend
181 hours in labor and
$580 in material for refinishing tables. How many tables should they plan to refinish with each method?

Solution

Let x be the number of tables finished with method 1 and y be the number of tables finished with method 2.

Hours?

1.5x +2.5y=181

x= (181-2.5y)/1.5

Cost?

9x +4y = 580

9((181-2.5y)/1.5)) +4y =580

To simplify divide the 9 with 1.5. You get  6. Therefore it becomes

6(181-2.5y) +4y =580

1086  - 15y + 4y =580

1086-580=15y-4y

11y=506

y=46

Use the value to find the value of x

1.5x +2.5(46)=181

1.5x +115 =181

1.5x = 66

x=66/1.5

x=44


So they should make 44 tables using method 1 and 46 tables using method 2.

Please let me know if you need any clarification. I'm always happy to answer your questions.
Sep 28th, 2015

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