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A young sumo wrestler decided to go on a special high-protein diet to gain weight rapidly and at a constant rate. After 8 months, he weighed 138 kilograms. He started at 90 kilograms. Let y represent the sumo wrestler's weight (in kilograms) after x months. Complete the equation for the relationship between the weight and number of months. y=

A young sumo wrestler decided to go on a special high-protein diet to gain weight rapidly and at a constant rate. After 88 months, he weighed 138138 kilograms. He started at 9090 kilograms.\newlineLet y y represent the sumo wrestler's weight (in kilograms) after x x months.\newlineComplete the equation for the relationship between the weight and number of months.\newliney=□ y=\square

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Q. A young sumo wrestler decided to go on a special high-protein diet to gain weight rapidly and at a constant rate. After 88 months, he weighed 138138 kilograms. He started at 9090 kilograms.\newlineLet y y represent the sumo wrestler's weight (in kilograms) after x x months.\newlineComplete the equation for the relationship between the weight and number of months.\newliney=□ y=\square
  1. Determining the rate of weight gain: First, let's determine the rate of weight gain per month.\newlineThe sumo wrestler started at 9090 kilograms and after 88 months weighed 138138 kilograms.\newlineTo find the rate of weight gain, we subtract the starting weight from the final weight and then divide by the number of months.\newlineRate of weight gain per month = Final weight−Starting weightNumber of months\frac{\text{Final weight} - \text{Starting weight}}{\text{Number of months}}\newlineRate of weight gain per month = 138 kg−90 kg8 months\frac{138 \text{ kg} - 90 \text{ kg}}{8 \text{ months}}\newlineRate of weight gain per month = 48 kg8 months\frac{48 \text{ kg}}{8 \text{ months}}\newlineRate of weight gain per month = 66 kg/month
  2. Writing the equation for the sumo wrestler's weight: Now that we have the rate of weight gain, we can write the equation for the sumo wrestler's weight after xx months.\newlineThe equation will be in the form of a linear equation y=mx+by = mx + b, where mm is the rate of weight gain per month, and bb is the starting weight.\newlineSince we know the rate of weight gain is 6 kg/month6\,\text{kg/month} and the starting weight is 90 kg90\,\text{kg}, the equation is:\newliney=6x+90y = 6x + 90
  3. Checking the equation with the given data: Let's check the equation with the given data to ensure there are no math errors.\newlineIf we substitute x=8x = 8 months into the equation, we should get the sumo wrestler's weight after 88 months, which is 138138 kg.\newliney=6(8)+90y = 6(8) + 90\newliney=48+90y = 48 + 90\newliney=138y = 138 kg\newlineThis matches the given information, so the equation is correct.

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