Explanation:
x = cost of 1 kg mushrooms
y = cost of 1 kg turnips
2x + 2.5y = 8.55
3x + 4y = 13.10
so, we have a system of 2 equations with 2 variables.
this can be solved either by
- substitution (we use one equation to express one variable by the other, and use that result in the second equation to solve for the second variable, and then use that result again in the first equation to solve for the first variable)
or by
- elimination (we multiply both equations by fitting factors, so that then the sum of both results delivers one equation with one remaining variable. that result we use then in any of the original equations to solve for the other variable).
this here looks (for me) better for elimination.
we bring the first equation to something with 6x, and the second one to something with -6x, abd then we add them.
so, we multiply the first equation by 3, and the second equation by -2 :
6x + 7.5y = 25.65
-6x - 8y = -26.20
-------------------------------
0 -0.5y = -0.55
y = -0.55/-0.5 = £1.10
for x I suggest now to use the second original equation :
3x + 4y = 13.10
3x + 4×1.10 = 13.10
3x + 4.40 = 13.10
3x = 8.70
x = 8.70/3 = £2.90
a) 1 kg of turnips cost £2.90
b) 1 kg if mushrooms cost £1.10