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A young sumo wrestler decided to go on a special high-protein diet to gain weight rapidly. After 11 months, he weighed 140 kilograms. He gained weight at a rate of 5.5 kilograms per month.
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. After $11$ months, he weighed $140$ kilograms. He gained weight at a rate of $5.5$ kilograms per month. $\newline$ Let $y$ represent the sumo wrestler's weight (in kilograms) after $x$ months. $\newline$ Complete the equation for the relationship between the weight and number of months. $\newline$ $y=\square$

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Write a linear function: word problems

Full solution

Q. A young sumo wrestler decided to go on a special high-protein diet to gain weight rapidly. After

11

months, he weighed

140

kilograms. He gained weight at a rate of

5.5

kilograms per month.

\newline

Let

y

represent the sumo wrestler's weight (in kilograms) after

x

months.

\newline

Complete the equation for the relationship between the weight and number of months.

\newline

y=\square

Identify initial weight: Identify the initial weight of the sumo wrestler. $\newline$ Since the sumo wrestler gained weight over $11$ months, we need to find out his initial weight before he started gaining weight. $\newline$ We know that he gained $5.5$ kilograms each month for $11$ months, which totals $5.5 \, \text{kg/month} \times 11 \, \text{months} = 60.5$ kilograms. $\newline$ To find the initial weight, we subtract the total weight gained from his weight after $11$ months. $\newline$ Initial weight $=$ Final weight $-$ Weight gained $\newline$ Initial weight $= 140 \, \text{kg} - 60.5 \, \text{kg}$
Calculate initial weight: Calculate the initial weight. $\newline$ Initial weight = $140\,\text{kg} - 60.5\,\text{kg}$ $\newline$ Initial weight = $79.5\,\text{kg}$ $\newline$ This is the weight of the sumo wrestler before he started the diet.
Write equation for weight: Write the equation for the sumo wrestler's weight after $x$ months. $\newline$ We know that the sumo wrestler gains $5.5$ kilograms each month. Therefore, the weight after $x$ months can be calculated by adding the weight gained over $x$ months to the initial weight. $\newline$ Weight after $x$ months = Initial weight + (Weight gained per month * Number of months) $\newline$ $y =$ Initial weight + $(5.5 \, \text{kg/month} \times x)$
Substitute initial weight: Substitute the initial weight into the equation. $\newline$ We have already calculated the initial weight to be $79.5\,\text{kg}$ . $\newline$ $y = 79.5\,\text{kg} + (5.5\,\text{kg}/\text{month} \times x)$ $\newline$ This is the equation that represents the sumo wrestler's weight after $x$ months.

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