Final answer:
To find the costs, we set up two equations based on the given data. Using elimination, we first determine the cost of 1 kg of carrots and then the cost of 1 kg of potatoes. The final costs are $2 per kg for potatoes and $2.40 per kg for carrots.
Step-by-step explanation:
The student's question involves solving a system of linear equations to determine the cost of potatoes and carrots per kilogram. We can set up two equations from the given information:
8 kg of potatoes (8P) + 5 kg of carrots (5C) = $28
2 kg of potatoes (2P) + 3 kg of carrots (3C) = $11.20
These equations can be solved using either substitution or elimination methods to find the price per kilogram (P and C) for potatoes and carrots, respectively.
Let's use the elimination method:
Multiply the second equation by 4 to align the potato coefficient with the first equation:
8 kg of potatoes (8P) + 5 kg of carrots (5C) = $28
8 kg of potatoes (8P) + 12 kg of carrots (12C) = $44.80
Now subtract the first equation from the modified second equation:
(8P + 12C) - (8P + 5C) = $44.80 - $28
7C = $16.80
Divide by 7 to find the price per kilogram of carrots:
C = $2.40
Substitute the value of C into the first equation and solve for P:
8P + 5($2.40) = $28
8P + $12 = $28
8P = $16
P = $2
The cost of 1 kg of potatoes is $2 and the cost of 1 kg of carrots is $2.40.