The total cost of 3 tables and 2 chairs is ₹1850. if a table costs ₹75 more than a chair, Find the price of chair

Answer

To solve the problem step-by-step, we will define variables, set up equations based on the information given, and solve for the price of the chair.

### Step 1: Define the Variables
Let the price of a chair be ₹X.
Let the price of a table be ₹Y.

### Step 2: Set Up the Equations
From the problem, we know two things:
1. The total cost of 3 tables and 2 chairs is ₹1850.
This can be expressed as:
\[ 3Y + 2X = 1850 \quad \text{(Equation 1)} \]

2. A table costs ₹75 more than a chair.
This can be expressed as:
\[ Y = X + 75 \quad \text{(Equation 2)} \]

### Step 3: Substitute Equation 2 into Equation 1
Now we will substitute the value of Y from Equation 2 into Equation 1:
\[ 3(X + 75) + 2X = 1850 \]

### Step 4: Simplify the Equation
Distributing the 3 in the equation:
\[ 3X + 225 + 2X = 1850 \]
Combining like terms:
\[ 5X + 225 = 1850 \]

### Step 5: Isolate the Variable
Now, we will isolate X by subtracting 225 from both sides:
\[ 5X = 1850 - 225 \]
Calculating the right side:
\[ 5X = 1625 \]

### Step 6: Solve for X
Now, divide both sides by 5 to find the value of X:
\[ X = \frac{1625}{5} \]
Calculating the division:
\[ X = 325 \]

### Step 7: Conclusion
The price of the chair is ₹325.

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