if shubham's father bought three oranges for apples and five bananas for rs 62 and his sister pinky bought 4 oranges 5 apples and 4 bananas for rs 72 then what amount did billu pay for one orange to apple and 7 bananas

To solve the problem, we need to determine the prices of the oranges, apples, and bananas individually. Let's denote the prices as follows:

- Let the price of one orange be \( x \) rupees.
- Let the price of one apple be \( y \) rupees.
- Let the price of one banana be \( z \) rupees.

From the problem, we are given the following information:

1. Shubham's father bought three oranges and five bananas for Rs 62.
   \[
   3x + 5z = 62
   \]

2. Pinky bought four oranges, five apples, and four bananas for Rs 72.
   \[
   4x + 5y + 4z = 72
   \]

We need to find the amount Billu paid for one orange, one apple, and seven bananas.

Let's denote the total amount Billu paid as \( T \). So,
\[
T = x + y + 7z
\]

To find \( T \), we need to solve for \( x \), \( y \), and \( z \) using the given equations. 

Let's rewrite the equations for clarity:
1. \( 3x + 5z = 62 \)
2. \( 4x + 5y + 4z = 72 \)

First, we solve equation 1 for \( z \) in terms of \( x \):
\[
z = \frac{62 - 3x}{5}
\]

Next, substitute \( z \) into equation 2:
\[
4x + 5y + 4 \left( \frac{62 - 3x}{5} \right) = 72
\]

Simplify and solve for \( y \):
\[
4x + 5y + \frac{4(62 - 3x)}{5} = 72
\]
\[
4x + 5y + \frac{248 - 12x}{5} = 72
\]
Multiply through by 5 to clear the fraction:
\[
20x + 25y + 248 - 12x = 360
\]
\[
8x + 25y = 112
\]
\[
25y = 112 - 8x
\]
\[
y = \frac{112 - 8x}{25}
\]

We now have expressions for \( y \) and \( z \) in terms of \( x \):
\[
z = \frac{62 - 3x}{5}
\]
\[
y = \frac{112 - 8x}{25}
\]

We substitute \( x \), \( y \), and \( z \) back into the equation for \( T \):
\[
T = x + \frac{112 - 8x}{25} + 7 \left( \frac{62 - 3x}{5} \right)
\]

Simplify and combine terms:
\[
T = x + \frac{112 - 8x}{25} + \frac{7(62 - 3x)}{5}
\]
\[
T = x + \frac{112 - 8x}{25} + \frac{434 - 21x}{5}
\]

Next, to combine these fractions, we need a common denominator. Let's express everything with the denominator 25:
\[
T = x + \frac{112 - 8x}{25} + \frac{5(434 - 21x)}{25}
\]
\[
T = x + \frac{112 - 8x + 2170 - 105x}{25}
\]
\[
T = x + \frac{2282 - 113x}{25}
\]

Combine the terms:
\[
T = x + 91.28 - 4.52x
\]
\[
T = 91.28 - 3.52x
\]

We need a bit more simplification and solving, so let's ensure calculations are correct or re-adjust to find specific values for \( x \), \( y \), and \( z \). Given the complexity, the result appears to be part-way simplified; verifying these would need substitution back into initial equations for accuracy check.

Would you like a more detailed step-by-step breakdown of solving this or have any specific part clarified?

**8 Related Questions:**
1. What would be the individual cost of one orange if only apples and bananas are known?
2. How does changing the number of bananas affect the total price?
3. What if Shubham's father bought four oranges instead? How would that change the equation?
4. How to solve simultaneous equations with three variables using substitution?
5. What other methods can be used to solve these types of equations?
6. Can we verify these values using another method, such as matrix operations?
7. What if Pinky bought two more apples, how would the total cost change?
8. How does understanding linear equations help in real-life budgeting?

**Tip:** Solving simultaneous equations often requires multiple steps; ensure each step is verified by substituting back into the original equations for accuracy.

Learn how to calculate the cost of oranges, apples, and bananas based on given purchase details. This problem involves solving simultaneous linear equations using the substitution method to find individual fruit prices. Suitable for students in Grades 9-12.

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