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This problem can be approached by solving a system of equations. Let's define two variables:

- Let \( x \) be the cost of one potted plant.
- Let \( y \) be the cost of one bag of fertilizer.

We are given the following information in the problem:

1. The cost of 7 potted plants and 2 bags of fertilizer is £43:
   \[
   7x + 2y = 43
   \]
   
2. The cost of 5 potted plants and 4 bags of fertilizer is £41:
   \[
   5x + 4y = 41
   \]

We need to solve these two equations to find \( x \) and \( y \), and then use those values to find the total cost when Louis buys 2 potted plants and 5 bags of fertilizer.

### Step 1: Solve the system of equations
We'll use the method of elimination or substitution to solve this system. 

First, multiply the first equation by 2 to align the coefficients of \( y \):
\[
14x + 4y = 86
\]

Now subtract the second equation \( 5x + 4y = 41 \) from this new equation:
\[
(14x + 4y) - (5x + 4y) = 86 - 41
\]
\[
9x = 45
\]
\[
x = 5
\]

### Step 2: Substitute \( x = 5 \) into one of the original equations
We'll substitute \( x = 5 \) into the first equation \( 7x + 2y = 43 \):
\[
7(5) + 2y = 43
\]
\[
35 + 2y = 43
\]
\[
2y = 43 - 35
\]
\[
2y = 8
\]
\[
y = 4
\]

### Step 3: Calculate the cost for Louis
Now that we know \( x = 5 \) and \( y = 4 \), we can calculate the cost for 2 potted plants and 5 bags of fertilizer:
\[
2x + 5y = 2(5) + 5(4) = 10 + 20 = 30
\]

So, the total cost for Louis is **£30**.

Would you like further details or have any questions?

Here are some related questions:
1. How would the system of equations change if the number of items purchased changed?
2. What if Louis wanted to buy 3 potted plants and 2 bags of fertilizer instead?
3. How could we solve this problem using substitution instead of elimination?
4. What if the price of a potted plant increased by £1; how would that affect the cost?
5. How would the total cost change if Louis received a 10% discount on fertilizer?

**Tip:** For systems of linear equations, the elimination method is very efficient when you can easily cancel out one variable by aligning the coefficients.

The cost of 7 potted plants and 2 bags of fertilizer is £43. The cost of 5 potted plants and 4 bags of fertilizer is £41. How much will it cost Louis to buy 2 potted plants and 5 bags of fertilizer?

Learn how to solve a system of linear equations involving the cost of potted plants and fertilizer. Use algebraic methods like elimination or substitution to find the cost for 2 potted plants and 5 bags of fertilizer. Suitable for students in Grades 7-9.

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