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The problem states:

- 7 kg of carrots and 5 kg of tomatoes cost a total of 480 pence.
- The ratio of the cost of 1 kg of carrots to the cost of 1 kg of tomatoes is \( 5:9 \).
  
We are tasked with finding the cost of 1 kg of carrots and 1 kg of tomatoes.

### Let's define the following variables:

- Let \( x \) be the cost of 1 kg of carrots in pence.
- Let \( y \) be the cost of 1 kg of tomatoes in pence.

### From the ratio, we know:
\[
\frac{x}{y} = \frac{5}{9}
\]
This implies:
\[
x = \frac{5}{9}y
\]

### Total cost:
The total cost of 7 kg of carrots and 5 kg of tomatoes is 480 pence. Therefore, the equation becomes:
\[
7x + 5y = 480
\]

### Substituting \( x = \frac{5}{9}y \) into the total cost equation:
\[
7\left(\frac{5}{9}y\right) + 5y = 480
\]
Simplify:
\[
\frac{35}{9}y + 5y = 480
\]
Multiply everything by 9 to eliminate the denominator:
\[
35y + 45y = 4320
\]
\[
80y = 4320
\]
Now solve for \( y \):
\[
y = \frac{4320}{80} = 54
\]

Thus, the cost of 1 kg of tomatoes, \( y \), is 54 pence.

### To find \( x \):
\[
x = \frac{5}{9}y = \frac{5}{9} \times 54 = 30
\]

Thus, the cost of 1 kg of carrots, \( x \), is 30 pence.

### Final Answer:
- Cost of 1 kg of carrots: **30 pence**
- Cost of 1 kg of tomatoes: **54 pence**

Would you like further details, or do you have any questions? Here are some related questions to consider:

1. How can you solve similar ratio problems with different total amounts?
2. What would happen if the ratio were reversed (e.g., \(9:5\))?
3. How can you set up and solve such problems when you know the cost of one type of vegetable?
4. Can you solve the problem using different algebraic methods like substitution or elimination?
5. How would you approach this problem if given a different currency or unit of weight?

**Tip**: Always check if the problem involves ratios, and set up a proportional relationship before solving the full equation!

7 kg of carrots and 5 kg of tomatoes cost a total of 480 pence. The ratio of the cost of 1 kg of carrots to 1 kg of tomatoes is 5:9. Work out the cost of 1 kg of carrots and 1 kg of tomatoes.

Learn how to calculate the cost of 1 kg of carrots and 1 kg of tomatoes using a ratio of 5:9 and a total cost of 480 pence. This problem involves key algebraic concepts, including ratios and linear equations, suitable for students in Grades 7-9.

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