Question

A party rental company has chairs and tables for rent. The total cost to rent 2 chairs and 3 tables is $30. The total cost to rent 4 chairs and 8 tables is $77. What is the cost to rent each chair and each table?

Answer 1

The cost of renting chair is $2.25 and table is $8.5

Step-by-step explanation:

Let x be the cost of rent a chair

and

Let y be the cost of renting a table

Then

$2x+3y=30\ \ \ Eqn\ 1\\4x+8y=77\ \ \ \ Eqn\2\\Multiplying\ Eqn\ 1\ by\ 2\ and\ then\ subtracting\ from\ Eqn\ 2\\2(2x+3y)=2(30)\\4x+6y=60\\Subtraction\\4x+8y-(4x+6y) = 77-60\\4x+8y-4x-6y=17\\2y=17\\Dividing\ both\ sides\ by\ 2\\\frac{2y}{2}=\frac{17}{2}\\y= 8.5\\Putting\ y=8.5\ in\ eqn\ 1\\2x+3y=30\\2x+3(8.5)=30\\2x+25.5=30\\Subtracting\ 25.5\ from\ both\ sides\\2x+25.5-25.5=30-25.5\\2x=4.5\\Dividing\ both\ sides\ by\ 2\\\frac{2x}{2}=\frac{4.5}{2}\\y=2.25$

The cost of renting chair is $2.25 and table is $8.5

Keywords: Linear system of equations, Variables

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