Question

A party rental company has chairs and tables for rent. The total cost to rent 8 chairs and 3 tables is $38. The total cost to rent 2 chairs and 5 tables is $35. What is the cost to rent each chair and each table?

cost to rent each chair: $

cost to rent each table: $

Answer 1

Let c be the chairs and t be the tables.  This is a system of equations you are dealing with.  The first equation tells us that 8 chairs (8c) plus 3 tables (3t) cost $38.  So the equation is 8c + 3t = 38.  The second equation tells us that 2 chairs (2c) and 5 tables (5t) cost $35.  So that equation is 2c + 5t = $35.  Solve this system any way you'd like.  I used elimination and multiplied the second equation by -4 to get a new equation:  -8c - 20t = -140.  Now the 8c's eliminate one another leaving you with -17t = -102.  Solving for t gives you t = 6.  Now sub in that t value in either equation to give you that each chair costs $2.50

Answer 2

Hey!

Hope this helps...

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If we let c stand for the numbers of chairs, and t stand for number of tables

We also know that we can re-write 8 chairs and 3 tables is $38, to 8c + 3t = $38

And 2 chairs and 5 tables is $35, to 2c + 5t = 35

We also know that any number we find out, has to make both statements true...

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8c + 3t = 38

-

4*[2c + 5t = 35]  >  8c + 20t = 140

= 0c - 17t = -102

-17t = -102

t = 6

Each table is $6

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Now that we know that each table is $6, we can substitute 6 for t...

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8c + 3t = 38 > 8c + 3(6) = 38 > 8c + 18 = 38 > 8c = 20 > c = 2.50

2c + 5t = 35 > 2c + 5(6) = 35 > 2c + 30 = 35 > 2c = 5  >  c = 2.50

Each chair costs $2.50

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    =+= Check =+=

8c + 3t = 38 > 8(2.5) + 3(6) = 38 > 20 + 18 = 38 > 38 = 38

2c + 5t = 35 > 2(2.5) + 5(6) = 35 > 5 + 30 = 35 > 35 = 35

And we see that the numbers are correct!!!