A party rental company has chairs and tables to rent. There were two customers who rented both chairs and tables last week.

Question

The display below shows the number of chairs, the number of tables, and the total cost (in dollars) for those two customers.

First customer: 3 chairs, 2 tables, Total cost (in dollars): 17

Second customer: 8 chairs, 3 tables, Total cost (in dollars): 37

(a) Write a system of equations that could be used to find the rental cost (in dollars) of each chair and each table.

(b) How much does each chair and each table cost (in dollars) to rent?

Answer 1

Let x=cost of chair

Let y=cost of table

1st customer 3x + 2y = 17

2nd customer 8x + 3y =37

If you multiply the 1st equation by 3 and the 2nd by -2 the y's will add to 0 and disappear.

9x + 6y = 51

-16x - 6y =-74

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-7x = -23 x = $3.29

substitute that value into one of the equations to find y

3(3.29) + 2y =17

9.87 + 2y = 17

2y=7.13 y = $3.56

chairs cost $3.29 and tables cost $3.56