"A trucking firm has 8 trucks, some carry a load of 10 tonnes and others carry a load of 5 tonnes. When all 8 trucks are carrying a full load, the total load is 70 tonnes." Develop and solve simultaneous equations to determine the number of trucks of each size that the trucking firm has.

total trucks: x+y = 8

total loads: 10x + 5y = 70

I expect you can solve that with little difficulty.

To solve this problem, we can set up a system of simultaneous equations to represent the given information.

Let's denote the number of trucks carrying a load of 10 tonnes as "x" and the number of trucks carrying a load of 5 tonnes as "y".

From the problem statement, we know that:
1. The trucking firm has a total of 8 trucks: x + y = 8

2. When all 8 trucks are carrying a full load, the total load is 70 tonnes: 10x + 5y = 70

Now, we have a system of two equations:

Equation 1: x + y = 8
Equation 2: 10x + 5y = 70

To solve this system of equations, we can either use substitution or elimination method.

Using the substitution method:
1. Solve equation 1 for x in terms of y: x = 8 - y
2. Substitute this value of x into equation 2: 10(8 - y) + 5y = 70
3. Simplify and solve for y: 80 - 10y + 5y = 70
-5y = 70 - 80
-5y = -10
y = -10 / -5
y = 2

Now, substitute the value of y back into equation 1 to solve for x:
x + 2 = 8
x = 8 - 2
x = 6

Therefore, the trucking firm has 6 trucks that carry a load of 10 tonnes and 2 trucks that carry a load of 5 tonnes.