SOLUTION: 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.

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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
-------------------------------
(1)
(2)
----------------------
Multiply both sides of (1) by
Multiply both sides of (2) by
Subtract (2) from (1)
---------------------------
(1)
(2)
---------------------------


and
(1)
(1)
(1)
(1)
---------------------
One table costs $70
One chair costs $20
----------------------
check:
(1)
(1)
(1)
(1)
OK you can check (2)




Answer by Lightning_Fast(78)   (Show Source): 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.
.
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)
.
Answer by ikleyn(52794)   (Show Source): You can put this solution on YOUR website!
.
Hey, the situation is much simpler than the two other tutors treat it. 

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.

That's it.



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