total cost for table and chairs

Question

a party rental company has chairs and tables for rent. the total cost to rent 3 chairs and 2 tables is $26. the total cost to rent 5 chairs and 6 tables is $72. what is the cost to rent each chair and each table?

Answer 1

c=cost of chairs

t=cost of tables

 

3c+2t=26

5c+6t=72

 

-3*(3c+2t)=26  *-3  To get one of the variables to cancel, you need opposites. multiplying this equation by -3 gives 6 and -6 as coefficients for t

 

-9c-6t=-78

5c+6t=72      add these down. Variables and the constants must match.

 

-4c=-6     divide both sides by -4

c=3/2      c =$1.50(per chair)

 

5(1.5)+6t=72      You can plug the value of c back into either equation.

7.5+6t=72

6t=64.5

t=$10.75(per table)

 

check-plug back into the other equation

3*1.5+2*10.75=26

26=26

Correct