Question 1068265: Two tables and 3 chairs together cost $200 whereas 3 tables and 2 chairs together cost $250. Find the cost of one table and one chair. Found 3 solutions by josmiceli, Lightning_Fast, ikleyn:Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website! Let = the cost of a table
Let = the cost of a chair
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(1)
(2)
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Multiply both sides of (1) by
Multiply both sides of (2) by
Subtract (2) from (1)
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(1)
(2)
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and
(1)
(1)
(1)
(1)
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One table costs $70
One chair costs $20
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check:
(1)
(1)
(1)
(1)
OK you can check (2)
You can put this solution on YOUR website! Let
T = table
C = chair
2T + 3C = 200 (200 dollars is the cost of 2 tables and 3 chairs)
3T + 2C = 250 (250 dollars is the cost of 3 tables and two chairs)
What is C + T?
Solve by substitution.
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Here, I got t=70
The table is 70$.
To find the chair, substitute the value back in any of the original equations.
I'll choose the first one
2(70)+3C=200
140+3C=200
3C=60
C=20
Chairs are 20$
Can also solve this graphically. If tables are x and chairs are y, we can find where the graphs intersect.
(this is essentially what we did above, but more visuals)
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The two equations are
2T + 3C = 200,
3T + 2C = 250.
Now add the two equations (both sides). You will get
5T + 5C = 450.
Now cancel the factor 5 in both sides. You will get
T + C = 90.
IT IS YOUR ANSWER: T + C = 90 dollars. One table and one chair cost 90 dollars.
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