Final answer:
The cost of 1 kg of mushrooms and 1 kg of turnips is $4.00.
Step-by-step explanation:
First, we need to set up a system of equations to represent the given information:
Let x be the cost of 1 kg of mushrooms and y be the cost of 1 kg of turnips.
From the first statement, the cost of 2 kg of mushrooms and 2.5 kg of turnips is 8.55. This can be written as:
2x + 2.5y = 8.55 (1)
From the second statement, the cost of 3 kg of mushrooms and 4 kg of turnips is 13.10. This can be written as:
3x + 4y = 13.10 (2)
Now, we can solve this system of equations using any method we prefer, such as substitution or elimination.
Let's use the elimination method:
Multiplying equation (1) by 4 and equation (2) by 2, we get:
8x + 10y = 34.20 (3)
6x + 8y = 26.20 (4)
Subtracting equation (4) from equation (3), we get:
8x + 10y - (6x + 8y) = 34.20 - 26.20
2x + 2y = 8.00 (5)
Now, we can solve equation (5) for y:
2y = 8.00 - 2x
y = 4.00 - x
Substituting this expression for y in equation (1):
2x + 2.5(4.00 - x) = 8.55
2x + 10.00 - 2.5x = 8.55
-0.5x = -1.45
x = 1.45 / 0.5
x = 2.90
Now, we can substitute the value of x into one of the original equations to find the value of y:
Let's use equation (1):
2(2.90) + 2.5y = 8.55
5.80 + 2.5y = 8.55
2.5y = 8.55 - 5.80
2.5y = 2.75
y = 2.75 / 2.5
y = 1.10
Therefore, the cost of 1 kg of mushrooms and 1 kg of turnips is $2.90 + $1.10 = $4.00.