To find the cost of 1 kg of carrots and the cost of 1 kg of tomatoes given the conditions, let's follow these steps.
1. Define the variables:
- Let the cost of 1 kg of carrots be [tex]\( C \)[/tex].
- Let the cost of 1 kg of tomatoes be [tex]\( T \)[/tex].
2. Set up the given ratio:
- According to the problem, the ratio of the cost of 1 kg of carrots to the cost of 1 kg of tomatoes is [tex]\( 5:9 \)[/tex].
- This can be written as [tex]\( \frac{C}{T} = \frac{5}{9} \)[/tex], which implies [tex]\( C = \frac{5}{9} T \)[/tex].
3. Set up the total cost equation:
- The total cost for 7 kg of carrots and 5 kg of tomatoes is given as 480 p.
- Therefore, we can write the equation:
[tex]\[ 7C + 5T = 480 \][/tex]
4. Substitute the ratio relation into the total cost equation:
- Substitute [tex]\( C = \frac{5}{9} T \)[/tex] into the total cost equation:
[tex]\[ 7 \left( \frac{5}{9} T \right) + 5T = 480 \][/tex]
5. Solve for [tex]\( T \)[/tex]:
- Simplify the equation:
[tex]\[ \frac{35}{9} T + 5T = 480 \][/tex]
- To combine the terms, first convert 5T to a fraction with a common denominator:
[tex]\[ \frac{35}{9}T + \frac{45}{9}T = 480 \][/tex]
[tex]\[ \frac{80}{9}T = 480 \][/tex]
- Multiply both sides by [tex]\( \frac{9}{80} \)[/tex] to solve for [tex]\( T \)[/tex]:
[tex]\[ T = 480 \times \frac{9}{80} \][/tex]
[tex]\[ T = 54 \][/tex]
6. Find the value of [tex]\( C \)[/tex]:
- Now that we have [tex]\( T \)[/tex], use the ratio relation to find [tex]\( C \)[/tex]:
[tex]\[ C = \frac{5}{9}T \][/tex]
[tex]\[ C = \frac{5}{9} \times 54 \][/tex]
[tex]\[ C = 30 \][/tex]
Therefore, the cost of 1 kg of carrots is 30 p, and the cost of 1 kg of tomatoes is 54 p.
