Question

Two young sumo wrestlers decided to go on a special diet to gain weight rapidly. They each gained weight at a constant rate.
The weight (in kilograms)
of the first wrestler as a function of time (in months) is given by the following table of values:


The graph of the weight (in kilograms) of the second wrestler as a function of time (in months) is shown below.


Which wrestler weighed more at the beginning of the diet? Select)
Which wrestler gained weight more quickly
Sclect

Answer 1

Answer:

1. The first wrestler weighed more at the beginning of the diet.
2. The second wrestler gains weight more quickly.

Step-by-step explanation:

For the first wrestler, we can see that from month $3$ to $4.5$, the wrestler's weight gets to be from $95$ kilograms to $101.75$ kilograms. This means that the diet made the wrestler gain $\red{6.75}$ kilograms of weight every $\red{1.5}$ month. We can also see that it's consistent with from month $4.5$ to $6$.

For the second wrestler, we can see on the graph that the diet makes the wrestler gain weight in linear fashion. This means that their weight gain is consistent. Let's find how much the wrestler is gaining weight for every $1.5$ months. At the moment when the wrestler started to diet, their weight is $\red{75}$ kilograms. At month $1.5$, we can see that the wrestler's weight is $82.5$. Now we can see that the wrestler gains $\blue{7.5}$ kilograms of weight every $\blue{1.5}$ months.

The first wrestler gains $\red{6.75}$ kilograms of weight every $\red{1.5}$ month while the second wrestler gains $\blue{7.5}$ kilograms of weight every $1.5$ months. The second wrestler gains weight more quickly.

The second wrestler weighed $\blue{75}$ at the beginning of the diet. We are not provided of weight of the first wrestler when they started dieting but we do know that they gain $\red{6.75}$ kilograms of weight every $1.5$ months. The first wrestler must weigh twice of $\red{6.75}$ kilograms of $95$ kilograms because month $3$ is twice $1.5$ months.

$\red{90 -6.75 \cdot 2} \\ \red{90 -13.5} \\ \red{76.5}$

The first wrestler weighed more at the beginning of the diet.

Answer 2

Answer:

The first wrestler weighed more at the beginning of the diet.

The second wrestler gains weight more quickly.

Step-by-step explanation:

For the first wrestler, we can see that from month  to , the wrestler's weight gets to be from  kilograms to  kilograms. This means that the diet made the wrestler gain  kilograms of weight every  month. We can also see that it's consistent with from month  to .

For the second wrestler, we can see on the graph that the diet makes the wrestler gain weight in linear fashion. This means that their weight gain is consistent. Let's find how much the wrestler is gaining weight for every  months. At the moment when the wrestler started to diet, their weight is  kilograms. At month , we can see that the wrestler's weight is . Now we can see that the wrestler gains  kilograms of weight every  months.

The first wrestler gains  kilograms of weight every  month while the second wrestler gains  kilograms of weight every  months. The second wrestler gains weight more quickly.

The second wrestler weighed  at the beginning of the diet. We are not provided of weight of the first wrestler when they started dieting but we do know that they gain  kilograms of weight every  months. The first wrestler must weigh twice of  kilograms of  kilograms because month  is twice  months.

The first wrestler weighed more at the beginning of the diet.