Final answer:
To find the cost of 1kg carrots and 1kg radishes, we create a system of linear equations based on the cost of radishes and carrots given in the problem. We then manipulate these equations to solve for R (cost of radishes per kg) and C (cost of carrots per kg). Finally, we solve these equations simultaneously to find the individual costs.
Step-by-step explanation:
The question involves solving a system of linear equations to find the cost of 1kg of carrots and 1kg of radishes. We can start by setting up two equations based on the information provided:
- Equation 1: 4R + 1.5C = 14.8
- Equation 2: 3R + 2C = 12.5
Where R is the cost per kg of radishes and C is the cost per kg of carrots. By solving these equations simultaneously, we can find the values of R and C. Let's multiply the second equation by 2 and the first by 3 to eliminate the C terms:
- 3*(Equation 1): 12R + 4.5C = 44.4
- 2*(Equation 2): 6R + 4C = 25
Now we can subtract the modified second equation from the modified first equation to solve for R:
- (3*Equation 1) - (2*Equation 2): (12R - 6R) + (4.5C - 4C) = 44.4 - 25
- 6R + 0.5C = 19.4
Substituting R back into the first equation, we find:
- 4R + 1.5C = 14.8
- C = (14.8 - 4R) / 1.5
Now place that expression of C into our new equation (6R + 0.5C = 19.4) and solve for R. Once R is found, we can find C and thus have the cost per kg for each of radishes and carrots.