SOLUTION: A party rental company has chairs and tables for rent. The total cost to rent 3 chairs and 5 tables is $57. The total cost to rent 12 chairs and 2 tables is $39.
What is the cost
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What is the cost
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Question 1189806: A party rental company has chairs and tables for rent. The total cost to rent 3 chairs and 5 tables is $57. The total cost to rent 12 chairs and 2 tables is $39.
What is the cost to rent each chair and each table? Found 2 solutions by math_tutor2020, ikleyn:Answer by math_tutor2020(3817) (Show Source):
The total cost to rent 3 chairs and 5 tables is $37
It leads to the equation of
3x+5y = 37
Another equation we can form is
12x+2y = 39
because 12 chairs (12x dollars) and 2 tables (2y dollars) cost 39 dollars combined
Let's solve for y in the second equation
12x+2y = 39
2y = 39-12x
y = (39-12x)/2
y = (39/2)-(12x/2)
y = 19.5 - 6x
Then we can plug it into the first equation to solve for x
3x+5y = 57
3x+5(19.5 - 6x) = 57
3x+97.5 - 30x = 57
-27x+97.5 = 57
-27x = 57-97.5
-27x = -40.5
x = (-40.5)/(-27)
x = 1.50
That decimal value is exact.
Then we can use this x value to find y
y = 19.5 - 6x
y = 19.5 - 6(1.50)
y = 19.5 - 9
y = 10.50
That decimal is exact as well
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Answers:
One chair costs $1.50 to rent
One table costs $10.50 to rent
You can put this solution on YOUR website! .
A party rental company has chairs and tables for rent.
The total cost to rent 3 chairs and 5 tables is $57. The total cost to rent 12 chairs and 2 tables is $39.
What is the cost to rent each chair and each table?
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Let x be the cost to rent a chair;
let y be the cost to rent a table.
Write two equations for two unknowns as you read the problem
3x + 5y = 57 (1)
12x + 2y = 39 (2)
This system is good to solve it by Elimination. For it, multiply equation (1) by 4 (both sides).
Keep equation (2) as is. Then you have this modified system
12x + 20y = 4*57 (3)
12x + 2y = 39 (4)
Now subtract equation (4) from equation (3). The terms with "x" will delete each other,
and you will get an equation for single unknown "y"
20y - 2y = 4*57 - 39
Simplify and find y
18y = 189
y = 189/18 = 10.50 dollars.
Then from equation (2) find
12x + 2*10.50 = 39
12x = 39 - 21 = 18
x = 18/12 = 1.50 dollars.
ANSWER. It cost $10.50 to rent one table and $1.50 to rent one chair.
CHECK. To check, substitute the found values into original equations:
Eq(1): 3*1.50 + 5*10.50 = 57 dollars, correct.
Eq(2): 12*1.50 + 2*10.50 = 39 dollars, correct.
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