I prefer to think of this graphically. The weight is rising steadily so it is represented by a straight line (y = mx + c), where time is on the x-axis and mass is on the y-axis. We have been given two co-ordinates on this graph, (4, 100) and (14, 160). We need to find the equation of this graph.
First, realise that the gradient of a linear graph (m) is equal to the change in y over the change in x (Δy/Δx) - the change is just the difference between the two points:
Δy/Δx = (160-100)/(14-4) = 60/10 = 6
This gradient value can now be substituted into the general formula:
y = 6x + c
Next we need to find the constant value, or y-intercept (c). To do this, substitute in one of the sets of coordinates we have been given in the question, where the number of months is x and the mass is y (I'm going to use 4 months and 100kg). Then, solve for c:
y = 6x + c
100 = (6*4) + c
100 = 24 + c
c = 100 - 24 = 76
Now we know the full equation of the graph - y = 6x + 76. The question asks us to find the mass of the wrestler before putting on weight; this is represented by x=0 on the graph, because the x-axis represents time. Therefore, substitute x=0 into the equation to find the y value (the mass of the wrestler):
y = 6x + 76
y = (6*0) + 76 = 76kg
The initial mass of the wrestler was 76kg
I hope this helps
