Question

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?

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