Question

A party rental company has chairs and tables for rent. The total cost to rent 5 chairs and 2 tables is $23 . The total cost to rent 3 chairs and 8 tables is $58. What is the cost to rent each chair and each table?

-Cost to rent each chair:$___
-Cost to rent each table:$___

Answer 1

• chair: $2.00
• table: $6.50

Explanation:

The two different rentals give rise to two equations. Let t and c represent the rental costs of a table and chair, respectively. The rentals are ...

5c +2t = 23

3c +8t = 58

Cramer's rule tells you ...

c = (2·58 -8·23)/(2·3-8·5) = -68/-34 = 2.00

t = (23·3 -58·5)/-34 = -221/-34 = 6.50

The cost to rent each chair is $2.00.

The cost to rent each table is $6.50.

_____

Cramer's Rule says the solution to

ax +by = c

dx +ey = g

is ...

x = (bg -ec)/(bd -ea)

y = (cd -ga)/(bd -ea)

When the equation's coefficients are not convenient to achieve elimination of a variable, Cramer's rule can get to the solution very quickly. The same number of math operations are involved, but they are expressed in terms of a formula that can be used with no guesswork.