a hardware store sells 3 litre cans of paint for £15 and 5 litre cans of paint for £20. In one day he sells 71 litres of paint worth a total of £320. How many cans of paint did the store sell?

Let the number of 3-litre cans sold be \( x \), and the number of 5-litre cans sold be \( y \).

We have two equations based on the given information:

1. The total number of litres of paint sold is 71 litres:
   \[
   3x + 5y = 71
   \]

2. The total amount of money from the sales is £320:
   \[
   15x + 20y = 320
   \]

### Solving the System of Equations

#### Step 1: Simplify the second equation
We can divide the second equation by 5 to make it simpler:
\[
3x + 4y = 64
\]

Now, we have the system:
\[
3x + 5y = 71
\]
\[
3x + 4y = 64
\]

#### Step 2: Subtract the second equation from the first
Subtract the second equation from the first to eliminate \( x \):
\[
(3x + 5y) - (3x + 4y) = 71 - 64
\]
\[
y = 7
\]

#### Step 3: Substitute \( y = 7 \) into one of the original equations
Substitute \( y = 7 \) into \( 3x + 5y = 71 \):
\[
3x + 5(7) = 71
\]
\[
3x + 35 = 71
\]
\[
3x = 36
\]
\[
x = 12
\]

### Conclusion
The store sold:
- 12 cans of 3-litre paint
- 7 cans of 5-litre paint

The total number of cans sold is:
\[
12 + 7 = 19 \text{ cans}
\]

Would you like more details on this solution?

### Follow-up questions:
1. What if the total litres sold were 80 instead of 71?
2. How would the price change if the store increased the price of the 5-litre cans?
3. Could there be fractional cans if the prices were adjusted?
4. How does changing the price per litre affect the number of cans sold?
5. Can you express this system graphically?

**Tip:** When solving systems of equations, simplifying one of the equations early on often makes calculations easier.

A hardware store sells 3-litre cans of paint for £15 and 5-litre cans of paint for £20. In one day he sells 71 litres of paint worth a total of £320. How many cans of paint did the store sell?

Learn how to solve a real-world problem using systems of linear equations. This problem involves determining the number of 3-litre and 5-litre paint cans sold based on litres and total sales. The solution uses key algebraic concepts like substitution and linear equations. Suitable for students in Grades 9-11.

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