Answer :
Answer:
1kg of carrots = 1.60
1kg of radishes = 3.10
Step-by-step explanation:
To solve the given problem, we can set up a system of linear equations based on the information provided. Let's denote the cost per kilogram of radishes as \( r \) and the cost per kilogram of carrots as \( c \).
From the first statement, we have the equation:
\[ 4r + 1.5c = 14.80 \]
This equation represents the total cost of 4 kg of radishes and 1.5 kg of carrots.
From the second statement, we have the equation:
\[ 3r + 2c = 12.50 \]
This equation represents the total cost of 3 kg of radishes and 2 kg of carrots.
Now, we have a system of two equations with two unknowns:
\[ \begin{cases} 4r + 1.5c = 14.80 \n 3r + 2c = 12.50 \end{cases}\]
To solve for \( c \) and \( r \), we can use the method of substitution or elimination. Let's use the elimination method by multiplying the second equation by 2 and the first equation by 3 to make the coefficients of \( c \) the same:
\[ \begin{cases} 12r + 4.5c = 44.40 \n 6r + 4c = 25 \end{cases} \]
Now, subtract the second equation from the first:
\[ (12r + 4.5c) - (6r + 4c) = 44.40 - 25 \]
\[ 6r + 0.5c = 19.40 \]
Now, we can solve for \( r \) by multiplying the entire equation by 2 to eliminate the decimal:
\[ 12r + c = 38.80 \]
\[ c = 38.80 - 12r \]
We can now substitute \( c \) back into one of the original equations to find \( r \). Let's use the second original equation:
\[ 3r + 2(38.80 - 12r) = 12.50 \]
\[ 3r + 77.60 - 24r = 12.50 \]
\[ -21r = 12.50 - 77.60 \]
\[ -21r = -65.10 \]
\[ r = (-65.10)/(-21) \]
\[ r = 3.10 \]
Now that we have the value of \( r \), we can find \( c \) by substituting \( r \) back into the equation we derived for \( c \):
\[ c = 38.80 - 12(3.10) \]
\[ c = 38.80 - 37.20 \]
\[ c = 1.60 \]
