SOLUTION: if 2 tables and 3 chairs cost Rs3500 and 3 tables and 2 chairs cost Rs 4000 what is the price of one table?

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Question 1097758: if 2 tables and 3 chairs cost Rs3500 and 3 tables and 2 chairs cost Rs 4000 what is the price of one table?
Answer by Theo(13342) About Me  (Show Source):
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let T represent the price of one table.
let C represent the price of 1 chair.

2T + 3C = 3500
3T + 2C = 4000

multiply both sides of the first equation by 3 and multiply both sides of the second equation by 2 to get:

6T + 9C = 10500
6T + 4C = 8000

subtract the second equation from the first to get:

5C = 2500

solve for C to get C = 500.

use either one of the original equations and replace C with 500 and solve for T.

first original equation is 2T + 3C = 3500
replace C with 500 to get 2T + 1500 = 3500
subtract 1500 from both sides of this equation to get 2T = 2000
solve for T to get T = 1000

you have T = 1000 and C = 500.

go back to the original equations and evaluate to determine if the solution is correct.

2T + 3C = 3500 becomes 2*1000 + 3*500 = 3500 which becomes 2000 + 1500 = 3500 which becomes 3500 = 3500 which confirms the solution is correct for the first equation.

3T + 2C = 4000 becomes 3*1000 + 2*500 = 4000 which becomes 3000 + 1000 = 4000 which becomes 4000 = 4000 which confirms the solution is correct for the second equation.

the price of one table is rs 1000.