Q1. A bakery sells cakes and cookies. If the total number of items is 150 and the number of cakes is twice the number of cookies, how many cakes are there?
Solution:
Let the number of cookies be x. Then the number of cakes is 2x. The equation is x + 2x = 150. Solving gives 3x = 150, so x = 50. Therefore, cakes = 2x = 100.
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Q2. A bookstore sells novels and magazines. If the total number of books is 200 and the number of novels is 3 times the number of magazines, how many novels are there?
Solution:
Let the number of magazines be x. Then the number of novels is 3x. The equation is x + 3x = 200. Solving gives 4x = 200, so x = 50. Therefore, novels = 3x = 150.
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Q3. A school has 120 students. If the number of boys is twice the number of girls, how many boys are there?
Solution:
Let the number of girls be x. Then the number of boys is 2x. The equation is x + 2x = 120. Solving gives 3x = 120, so x = 40. Therefore, boys = 2x = 80.
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Q4. A school has boys and girls in the ratio of 5:3. If there are 64 students in total, how many girls are there?
Solution:
Let the number of girls be 3x and boys be 5x. The equation is 3x + 5x = 64. Solving gives 8x = 64, so x = 8. Therefore, girls = 3x = 24.
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Q5. A concert hall has 300 seats. If the number of reserved seats is 50 more than the number of general admission seats, how many reserved seats are there?
Solution:
Let the number of general admission seats be x. Then the number of reserved seats is x + 50. The equation is x + (x + 50) = 300. Solving gives 2x + 50 = 300, so 2x = 250, x = 125. Therefore, reserved seats = x + 50 = 175.
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Q6. A farmer has chickens and cows. If there are 50 animals in total and the number of cows is 10 more than the number of chickens, how many cows are there?
Solution:
Let the number of chickens be x. Then the number of cows is x + 10. The equation is x + (x + 10) = 50. Solving gives 2x + 10 = 50, so 2x = 40, x = 20. Therefore, cows = x + 10 = 30.
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Q7. A company produces pens and pencils. If the total production is 500 items and the number of pens is 4 times the number of pencils, how many pens are produced?
Solution:
Let the number of pencils be x. Then the number of pens is 4x. The equation is x + 4x = 500. Solving gives 5x = 500, so x = 100. Therefore, pens = 4x = 400.
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Q8. In a class, the ratio of boys to girls is 3:2. If there are 25 students in total, how many girls are there?
Solution:
Let the number of girls be 2x and boys be 3x. The equation is 2x + 3x = 25. Solving gives 5x = 25, so x = 5. Therefore, girls = 2x = 10.
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Q9. A fruit seller has apples and oranges. If the total number of fruits is 80 and the number of apples is 3 times the number of oranges, how many apples are there?
Solution:
Let the number of oranges be x. Then the number of apples is 3x. The equation is x + 3x = 80. Solving gives 4x = 80, so x = 20. Therefore, apples = 3x = 60.
