Addison painted her room. She had 50 square meters to paint, and she painted at a constant rate. After 2 hours of painting, she had 35 square meters left. Let y represent the area (in square meters) left to paint after x hours. Complete the equation for the relationship between the area and number of hours. y=

Determine area painted in 2 hours: Determine the amount of area painted in 2 hours. Addison started with 50 square meters and after 2 hours, she had 35 square meters left to paint. Amount of area painted in 2 hours = Initial area - Area left after 2 hours Amount of area painted in 2 hours = 50 - 35 Amount of area painted in 2 hours = 15 square metersCalculate rate of painting per hour: Calculate the rate of painting per hour. Since Addison painted 15 square meters in 2 hours, her rate of painting is: Rate of painting = Amount of area painted / Time taken Rate of painting = 15 square meters / 2 hours Rate of painting = 7.5 square meters per hourWrite equation for area left to paint: Write the equation for the relationship between the area left to paint (y) and the number of hours (x). Since the rate of painting is constant, we can use it to find the area left to paint after any number of hours. Area left to paint after x hours = Initial area - (Rate of painting * Number of hours) y = 50 - 7.5x

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Addison painted her room. She had $50$ square meters to paint, and she painted at a constant rate. After $2$ hours of painting, she had $35$ square meters left. $\newline$ Let $y$ represent the area (in square meters) left to paint after $x$ hours. $\newline$ Complete the equation for the relationship between the area and number of hours. $\newline$ $y=$

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Math Problems

Grade 8

Write and solve equations for proportional relationships

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Q. Addison painted her room. She had

50

square meters to paint, and she painted at a constant rate. After

2

hours of painting, she had

35

square meters left.

\newline

Let

y

represent the area (in square meters) left to paint after

x

hours.

\newline

Complete the equation for the relationship between the area and number of hours.

\newline

y=

Determine area painted in $2$ hours: Determine the amount of area painted in $2$ hours. $\newline$ Addison started with $50 \text{ square meters}$ and after $2$ hours, she had $35 \text{ square meters}$ left to paint. $\newline$ Amount of area painted in $2$ hours $= \text{Initial area} - \text{Area left after 2 hours}$ $\newline$ Amount of area painted in $2$ hours $= 50 - 35$ $\newline$ Amount of area painted in $2$ hours $= 15 \text{ square meters}$
Calculate rate of painting per hour: Calculate the rate of painting per hour. $\newline$ Since Addison painted $15$ square meters in $2$ hours, her rate of painting is: $\newline$ Rate of painting = $\frac{\text{Amount of area painted}}{\text{Time taken}}$ $\newline$ Rate of painting = $\frac{15 \text{ square meters}}{2 \text{ hours}}$ $\newline$ Rate of painting = $7.5$ square meters per hour
Write equation for area left to paint: Write the equation for the relationship between the area left to paint $y$ and the number of hours $x$ . $\newline$ Since the rate of painting is constant, we can use it to find the area left to paint after any number of hours. $\newline$ Area left to paint after $x$ hours = Initial area - (Rate of painting $*$ Number of hours) $\newline$ $y = 50 - 7.5x$