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2 problems match “mixture problems”. Clear

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1. Share of total area from rose fractions ●●○○○ 20 ptsTwo fields are planted with roses and lavender. $65\%$ of the area of the first field is roses, $45\%$ of the area of the second field is roses, and $53\%$ of the area of both fields together is roses. What percentage of the total area (of both fields together) is the area of the first field?
2. Boys to girls ratio from averages ●●○○○ 20 ptsIn a math test, the average score of a class is 78 points, and the average scores of the boys and the girls are 75.5 points and 81 points, respectively. Write the ratio of the number of boys to the number of girls in the class as $a:b$ in lowest terms. Find $a$ and $b$.