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.