Sumo wrestlers in Japan are well known for their dedication, discipline, and very large bodies. A young sumo wrestler decides to go on a special high-protein diet to gain weight rapidly. After 4 months on this diet, his mass is 100 kilograms. After 14 months, his mass is 160 kilograms. Let's assume that the sumo wrestler's mass changes at a constant rate while he is on this special diet.
What was the wrestler's mass in kilograms when he began his diet?
Answer (2)
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
The sumo wrestler's mass when he began his high-protein diet was 76 kilograms. This was calculated by establishing a linear relationship between his mass and time based on the provided data points. The constant rate of gain was found to be 6 kg per month.
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