Answer :
Let the cost per kilogram of carrots be [tex]$5k$[/tex] and the cost per kilogram of tomatoes be [tex]$9k$[/tex], where [tex]$k$[/tex] is a constant.
The total cost for the carrots and tomatoes is given by
[tex]$$187(5k) + 5(9k) = 480.$$[/tex]
Step 1. Multiply out the terms:
[tex]$$187 \times 5k + 5 \times 9k = 480.$$[/tex]
Step 2. Simplify the equation:
[tex]$$k(187 \times 5 + 5 \times 9) = 480.$$[/tex]
Calculate the expression in the parentheses:
[tex]$$187 \times 5 = 935 \quad \text{and} \quad 5 \times 9 = 45,$$[/tex]
so
[tex]$$935 + 45 = 980.$$[/tex]
Thus, the equation becomes:
[tex]$$980k = 480.$$[/tex]
Step 3. Solve for [tex]$k$[/tex]:
[tex]$$k = \frac{480}{980} \approx 0.4897959183673469.$$[/tex]
Step 4. Now, calculate the cost per kilogram for each vegetable:
- For carrots:
[tex]$$\text{Cost per kg of carrots} = 5k \approx 5 \times 0.4897959183673469 \approx 2.4489795918367347 \, \text{pence}.$$[/tex]
- For tomatoes:
[tex]$$\text{Cost per kg of tomatoes} = 9k \approx 9 \times 0.4897959183673469 \approx 4.408163265306122 \, \text{pence}.$$[/tex]
Thus, the cost of 1 kg of carrots is approximately [tex]$2.45$[/tex] pence, and the cost of 1 kg of tomatoes is approximately [tex]$4.41$[/tex] pence.
The total cost for the carrots and tomatoes is given by
[tex]$$187(5k) + 5(9k) = 480.$$[/tex]
Step 1. Multiply out the terms:
[tex]$$187 \times 5k + 5 \times 9k = 480.$$[/tex]
Step 2. Simplify the equation:
[tex]$$k(187 \times 5 + 5 \times 9) = 480.$$[/tex]
Calculate the expression in the parentheses:
[tex]$$187 \times 5 = 935 \quad \text{and} \quad 5 \times 9 = 45,$$[/tex]
so
[tex]$$935 + 45 = 980.$$[/tex]
Thus, the equation becomes:
[tex]$$980k = 480.$$[/tex]
Step 3. Solve for [tex]$k$[/tex]:
[tex]$$k = \frac{480}{980} \approx 0.4897959183673469.$$[/tex]
Step 4. Now, calculate the cost per kilogram for each vegetable:
- For carrots:
[tex]$$\text{Cost per kg of carrots} = 5k \approx 5 \times 0.4897959183673469 \approx 2.4489795918367347 \, \text{pence}.$$[/tex]
- For tomatoes:
[tex]$$\text{Cost per kg of tomatoes} = 9k \approx 9 \times 0.4897959183673469 \approx 4.408163265306122 \, \text{pence}.$$[/tex]
Thus, the cost of 1 kg of carrots is approximately [tex]$2.45$[/tex] pence, and the cost of 1 kg of tomatoes is approximately [tex]$4.41$[/tex] pence.
