3 pepsi and 1 mango juice bottles together cost RS .53 but 2 pepsi and 4 mango juice bottles  cost RS. 62 find the cost of a pepsi and a mango juice bottle

Let the cost of a Pepsi bottle be \( x \) and the cost of a Mango juice bottle be \( y \). We can set up the following system of equations based on the information provided:

1. \( 3x + y = 53 \)  (for 3 Pepsi and 1 Mango juice)
2. \( 2x + 4y = 62 \)  (for 2 Pepsi and 4 Mango juice)

### Step 1: Solve the system of equations

We can solve these equations by substitution or elimination. Let's use the elimination method.

From equation 1:
\[
3x + y = 53 \quad \text{(Equation 1)}
\]

Multiply Equation 1 by 4 to match the coefficients of \( y \) in both equations:
\[
4(3x + y) = 4(53)
\]
\[
12x + 4y = 212 \quad \text{(Equation 3)}
\]

Now subtract Equation 2 from Equation 3:
\[
(12x + 4y) - (2x + 4y) = 212 - 62
\]
\[
12x - 2x = 150
\]
\[
10x = 150
\]
\[
x = 15
\]

### Step 2: Find the value of \( y \)

Now that we know \( x = 15 \), substitute it back into Equation 1:
\[
3(15) + y = 53
\]
\[
45 + y = 53
\]
\[
y = 53 - 45
\]
\[
y = 8
\]

### Final Answer:
- The cost of a Pepsi bottle is **Rs. 15**.
- The cost of a Mango juice bottle is **Rs. 8**.

Would you like a more detailed explanation, or do you have any questions?

Here are 5 related questions:
1. How would the cost change if 5 Pepsi and 3 Mango juice bottles were purchased?
2. How can you verify the solution using substitution into the second equation?
3. What happens to the system of equations if the prices increase by 10%?
4. How would the equations change if the cost of Pepsi was reduced by Rs. 2?
5. Can you solve a similar system if only the total cost was given, but not the individual costs?

**Tip:** When solving systems of equations, ensure that the coefficients align when using the elimination method. This simplifies the calculation process.

3 Pepsi and 1 mango juice bottles together cost Rs. 53 but 2 Pepsi and 4 mango juice bottles cost Rs. 62. Find the cost of a Pepsi and a mango juice bottle.

Find the cost of a Pepsi and a Mango juice bottle by solving a system of linear equations. This problem uses algebraic concepts like substitution and the elimination method. A step-by-step solution is provided, suitable for students in Grades 8-10.

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