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Six litres of white paint are mixed with three litres of blue paint that costs per litre more. The total price of the mixture is . Find the price of the white paint.
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Q. Six litres of white paint are mixed with three litres of blue paint that costs per litre more. The total price of the mixture is . Find the price of the white paint.
- Denote Price per Litre: Let's denote the price per litre of white paint as dollars. Since the blue paint costs more per litre, the price per litre of blue paint will be W + \(\$2\). We have litres of white paint and litres of blue paint, making a total of litres of paint. The total cost of the paint is .
- Set Up Equation: We can set up the equation to represent the total cost of the mixture: + = \\(24\).
- Distribute Litres into Prices: Now, let's distribute the litres into the prices: \(6W + 3(W + (\$2)) = \$(24).\)
- Simplify Equation: Next, we simplify the equation: \(6W + 3W + (\$6) = (\$24).\)
- Combine Like Terms: Combine like terms: \(9W + (\$6) = (\$24)\).
- Isolate Terms with W: Subtract \(\$6\) from both sides to isolate the terms with W:\(\newline\)\(9W = \$24 - \$6\).
- Simplify Right Side: Simplify the right side of the equation: W = \$\(18\).
- Divide Both Sides: Divide both sides by \(9\) to solve for W:\(\newline\)\(W = \frac{\$18}{9}\).
- Calculate Value of W: Calculate the value of W:\(\newline\)\(W = \$2\).
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