Questions: Two artists, Mia and Noah, are working on separate mural projects. Mia has already painted 120 square meters of wall and continues to paint an additional 15 square meters per day. Noah starts with only 40 square meters painted but paints 25 square meters per day. If x represents the number of days they have been painting, after how many days will Mia and Noah have painted the same total amount of wall space? The equation that shows the relationship between the number of days, x, and the areas painted by Mia and Noah is

Two artists, Mia and Noah, are working on separate mural projects. Mia has already painted 120 square meters of wall and continues to paint an additional 15 square meters per day. Noah starts with only 40 square meters painted but paints 25 square meters per day. If x represents the number of days they have been painting, after how many days will Mia and Noah have painted the same total amount of wall space? The equation that shows the relationship between the number of days, x, and the areas painted by Mia and Noah is
Transcript text: Two artists, Mia and Noah, are working on separate mural projects. Mia has already painted 120 square meters of wall and continues to paint an additional 15 square meters per day. Noah starts with only 40 square meters painted but paints 25 square meters per day. If $x$ represents the number of days they have been painting, after how many days will Mia and Noah have painted the same total amount of wall space? The equation that shows the relationship between the number of days, $x$, and the areas painted by Mia and Noah is $\square$
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Solution

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Solution Steps

Step 1: Define the equations for Mia and Noah

Mia's total painted area after \( x \) days is given by: \[ \text{Mia's area} = 120 + 15x \]

Noah's total painted area after \( x \) days is given by: \[ \text{Noah's area} = 40 + 25x \]

Step 2: Set the equations equal to each other

To find the number of days \( x \) when Mia and Noah have painted the same total area, set the two equations equal: \[ 120 + 15x = 40 + 25x \]

Step 3: Solve for \( x \)

Subtract \( 15x \) from both sides: \[ 120 = 40 + 10x \]

Subtract \( 40 \) from both sides: \[ 80 = 10x \]

Divide both sides by \( 10 \): \[ x = 8 \]

Final Answer

\[ \boxed{x = 8} \]

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