Answer :
To solve this problem, we can use a system of equations. Let's denote:
- [tex]x[/tex] as the cost of one table
- [tex]y[/tex] as the cost of one chair
We are given the following two equations based on the problem statement:
[tex]5x + 2y = 3700[/tex]
[tex]2x + 5y = 2950[/tex]
We want to find the cost of 3 tables and 3 chairs, which means we need to find the value of [tex]3x + 3y[/tex].
Step 1: Solve the system of equations
First, let’s solve the system of equations to find [tex]x[/tex] and [tex]y[/tex].
Start with the two equations:
- [tex]5x + 2y = 3700[/tex]
- [tex]2x + 5y = 2950[/tex]
We can use the method of substitution or elimination. Here, we'll use elimination because it seems easier to eliminate a variable by making coefficients equal.
Let's eliminate [tex]x[/tex] by making the coefficients of [tex]x[/tex] in both equations equal. Multiply Equation 1 by 2 and Equation 2 by 5:
[tex]10x + 4y = 7400[/tex]
[tex]10x + 25y = 14750[/tex]
Now subtract the first new equation from the second:
[tex](10x + 25y) - (10x + 4y) = 14750 - 7400[/tex]
[tex]21y = 7350[/tex]
Divide both sides by 21:
[tex]y = \frac{7350}{21}[/tex]
[tex]y = 350[/tex]
Step 2: Substitute to find [tex]x[/tex]
Now that we know [tex]y = 350[/tex], substitute this back into one of the original equations to find [tex]x[/tex].
Use the first equation:
[tex]5x + 2(350) = 3700[/tex]
[tex]5x + 700 = 3700[/tex]
Subtract 700 from both sides:
[tex]5x = 3000[/tex]
Divide by 5:
[tex]x = 600[/tex]
Step 3: Calculate the cost of 3 tables and 3 chairs
Now, with [tex]x = 600[/tex] and [tex]y = 350[/tex], we can find the cost of 3 tables and 3 chairs:
[tex]3x + 3y = 3(600) + 3(350)[/tex]
[tex]= 1800 + 1050[/tex]
[tex]= 2850[/tex]
Thus, the cost of 3 tables and 3 chairs is Rs 2850.
