Math  /  Algebra

QuestionHiro painted his room. After 3 hours of painting at a rate of 8 square meters per hour, he had 28 square meters left to paint.
Let yy represent the area (in square meters) left to paint after xx hours.
Complete the equation for the relationship between the area and number of hours. y=y= \square
Show Calculator \square
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Studdy Solution

STEP 1

1. Hiro's painting rate is constant at 8 square meters per hour.
2. After 3 hours of painting, 28 square meters remain to be painted.
3. We need to establish a linear relationship between the area left to paint, y y , and the number of hours spent painting, x x .

STEP 2

1. Determine the total area to be painted.
2. Establish the relationship between the area left to paint and the number of hours spent painting.
3. Formulate the linear equation y=mx+c y = mx + c .

STEP 3

Calculate the area Hiro has painted after 3 hours. Area Painted=3×8=24 square meters \text{Area Painted} = 3 \times 8 = 24 \text{ square meters}

STEP 4

Determine the total area to be painted by adding the area painted to the area left to paint. Total Area=24+28=52 square meters \text{Total Area} = 24 + 28 = 52 \text{ square meters}

STEP 5

Express the area left to paint y y as a function of the number of hours x x spent painting. y=Total Area(Rate×Time) y = \text{Total Area} - (\text{Rate} \times \text{Time})

STEP 6

Substitute the known values (Total Area = 52 and Rate = 8 square meters per hour) into the equation. y=528x y = 52 - 8x

STEP 7

Verify the equation by checking if it satisfies the given condition (i.e., after 3 hours, 28 square meters remain to be painted). y=528×3=5224=28 y = 52 - 8 \times 3 = 52 - 24 = 28
Therefore, the relationship between the area left to paint y y and the number of hours spent painting x x is: y=528x y = 52 - 8x

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