Final answer:
The cost of 1kg of turnips is £2.14, and the cost of 1kg of mushrooms is £1.59. These values were determined by solving two simultaneous equations, representing the combined cost of mushrooms and turnips.
Step-by-step explanation:
To solve for the cost of 1kg of turnips and 1kg of mushrooms, we have two equations based on the information given:
2kg of mushrooms + 2.5kg of turnips = £8.55
3kg of mushrooms + 4kg of turnips = £13.10
Let's denote the cost of 1kg of mushrooms as M and the cost of 1kg of turnips as T. Hence the equations become:
2M + 2.5T = £8.55
3M + 4T = £13.10
To find the cost of 1kg of turnips (T) and 1kg of mushrooms (M), we can use simultaneous equations to solve for M and T.
Multiplying the first equation by 2 to eliminate T gives us:
4M + 5T = £17.10
We then multiply the second equation by 1.5 to make the coefficients of T the same:
4.5M + 6T = £19.65
Subtracting the second equation from 1.5 times the first one gives
1.5(2M + 2.5T) - (3M + 4T) = 1.5(£8.55) - £13.10
This simplifies to:
0.5M - 0.5T = £12.825 - £13.10 which simplifies to
0.5M - 0.5T = -£0.275
If we divide by 0.5, we get
M - T = -£0.55
Now we can substitute M - T = -£0.55 in the first original equation to find the value of T.
2(-£0.55 + T) + 2.5T = £8.55
-1.10 + 2T + 2.5T = £8.55
4.5T = £9.65
T = £2.14
Therefore, the cost of 1kg of turnips is £2.14. Once we have T, we can plug it back into the equation M - T = -£0.55 to find M. This gives us
M - £2.14 = -£0.55
M = -£0.55 + £2.14
M = £1.59
Thus, the cost of 1kg of mushrooms is £1.59.