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- The cost of ten apples, eight kiwis and 12 papaya is ₹240. The cost of eight apples, six kiwis and ten papayas is ₹ 180. Find the cost of one apple, one kiwi and one papaya.

# The cost of ten apples, eight kiwis and 12 papaya is ₹240. The cost of eight apples, six kiwis and ten papayas is ₹ 180. Find the cost of one apple, one kiwi and one papaya.

Crack the fruit math problem: Unravel the mystery of fruit prices with two equations. Find out how much one apple, one kiwi, and one papaya cost.

by Maivizhi A

**Updated **Mar 05, 2024

## The cost of ten apples, eight kiwis and 12 papaya is ₹240. The cost of eight apples, six kiwis and ten papayas is ₹ 180. Find the cost of one apple, one kiwi and one papaya.

Let's denote the cost of an apple, a kiwi, and a papaya as A, K, and P respectively.

We are given a system of two equations with three unknowns:

- 10A + 8K + 12P = 240 (Equation 1)
- 8A + 6K + 10P = 180 (Equation 2)

To solve for the cost of one apple, one kiwi, and one papaya (A + K + P), we need to eliminate one of the variables. Since we have two equations and three unknowns, eliminating one variable is possible.

Here, we can eliminate P by subtracting Equation 2 from Equation 1:

(1) 10A + 8K + 12P = 240

(-) (2) 8A + 6K + 10P = 180

2A + 2K + 2P = 60

Dividing both sides by 2, we get:

A + K + P = 30

Therefore, the cost of one apple, one kiwi, and one papaya is ₹30.

## Systems of Linear Equations

A system of linear equations is a collection of two or more **linear equations**, which involve the same **variables**. A linear equation is an equation where the highest power of each variable is **1**.

Here are some key points about systems of linear equations:

**Variables:**Each equation in the system involves the same set of variables. These variables represent unknown quantities that we want to solve for.**Solution:**A solution of a system of linear equations is a set of values for the variables that satisfies all the equations in the system simultaneously. In other words, if you plug these values into each equation, you get a true statement.**Number of solutions:**Depending on the relationships between the equations, a system can have:**One unique solution:**This is the most common case, where the lines (for 2 variables) or planes (for 3 variables) representing the equations intersect at a single point.**Infinitely many solutions:**This occurs when the equations represent lines (or planes) that completely overlap, indicating any point on that line (or plane) satisfies both equations.**No solution:**This happens when the lines (or planes) are parallel, indicating they never intersect.

### Example:

Here's an example of a system of linear equations in two variables:

**Equation 1:**2x + 3y = 5**Equation 2:**x - y = 1

This system can be solved using various methods like:

**Graphical method:**Plotting both equations and finding the point of intersection.**Substitution method:**Solving one equation for one variable and substituting it into the other equation to solve for the remaining variable.**Elimination method:**Manipulating the equations to eliminate one variable and then solving for the remaining variable.

These methods will help you find the solution, which in this case is:

**x = 2****y = 1**

## The cost of ten apples, eight kiwis and 12 papaya is ₹240. The cost of eight apples, six kiwis and ten papayas is ₹ 180. Find the cost of one apple, one kiwi and one papaya - FAQs

1. What is a system of linear equations?

A system of linear equations is a collection of two or more linear equations involving the same set of variables.

2. What do variables represent in a system of linear equations?

Variables represent unknown quantities that we aim to solve for in the equations.

3. What is a solution in the context of systems of linear equations?

A solution is a set of values for the variables that satisfies all equations in the system simultaneously.

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