Discover a world of knowledge at Westonci.ca, where experts and enthusiasts come together to answer your questions. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
Sagot :
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.
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.
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.