Sure, let's solve the problem step by step.
We are given the following information:
- The cost of 5 kg of oranges is the same as the cost of 3 kg of apples.
We need to find out how many kilograms of oranges are needed to exchange 9 kg of apples.
Here's how we can approach this problem:
1. Step 1: Set up a relationship between the cost of oranges and apples.
Let's define:
- `o` as the cost per kilogram of oranges
- `a` as the cost per kilogram of apples
According to the problem, the cost of 5 kg of oranges is the same as the cost of 3 kg of apples. This can be written as:
[tex]\[
5o = 3a
\][/tex]
2. Step 2: Solve for one variable in terms of the other.
For ease of calculations, let's solve the above equation for `a` in terms of `o`:
[tex]\[
a = \frac{5}{3}o
\][/tex]
3. Step 3: Relate the total cost of 9 kg of apples to the cost of oranges.
We need to find out how many kilograms of oranges (let's denote this by `x`) are equivalent in cost to 9 kg of apples. The cost of 9 kg of apples can be expressed as:
[tex]\[
9a = 9 \left(\frac{5}{3}o\right)
\][/tex]
4. Step 4: Simplify and solve for `x`.
Now, `x` kilograms of oranges should have the same cost as 9 kg of apples:
[tex]\[
xo = 9 \left(\frac{5}{3}o\right)
\][/tex]
Simplifying the right side, we get:
[tex]\[
xo = 15o
\][/tex]
Dividing both sides by `o` to isolate `x`, we find:
[tex]\[
x = 15
\][/tex]
Therefore, 15 kg of oranges are required to exchange for 9 kg of apples.
