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question:The denominator of a fraction is 7 less than X times the numerator. If the fraction is equivalent to 2/5, The numerator of the fraction is 14. What is the value of unknown variable X?

answer:To solve this problem, we need to determine the value of x, which represents the multiplier for the denominator of the fraction. We know that the numerator of the fraction is 14. The fraction is equivalent to 2/5. We can set up the equation as follows: Numerator / Denominator = 2 / 5 14 / (x * 14 - 7) = 2 / 5 Let's simplify and solve for x: 14 * 5 = 2 * (x * 14 - 7) 70 = 28x - 14 To isolate x, we add 14 to both sides of the equation: 70 + 14 = 28x - 14 + 14 84 = 28x To solve for x, we divide both sides of the equation by 28: x = 84 / 28 x = 3 The value of x is 3. The answer is: 3

question:Gunther needs to clean his apartment. It takes him 45 minutes to vacuum the carpets, 60 minutes to dust the furniture, 30 minutes to mop the floors in his kitchen, and 5 minutes to brush each cat, and he has three cats. If he has 3 hours of free time available, and he uses this time to clean his apartment, how many minutes of free time will he have left after he cleans the apartment?

answer:To calculate the total time Gunther will spend cleaning, we add up the time it takes for each task: 45 minutes + 60 minutes + 30 minutes + (5 minutes x 3 cats) = 45 + 60 + 30 + 15 = 150 minutes. Since there are 60 minutes in an hour, Gunther has 3 hours x 60 minutes = 180 minutes of free time. If he spends 150 minutes cleaning, he will have 180 minutes - 150 minutes = 30 minutes of free time left. 30 The answer is: 30

question:Five friends eat at Wendy's and ordered the following: a platter of Taco Salad that cost 10, 5 orders of Dave's Single hamburger that cost 5 each, x sets of french fries that cost 2.50, and 5 cups of peach lemonade that cost 2 each. How much will each of them pay if they will split the bill equally? If we know the answer to the above question is 11, what is the value of unknown variable x?

answer:The platter of Taco Salad costs 10. The 5 orders of Dave's Single hamburger cost 5 * 5 = 25. The 5 cups of peach lemonade cost 5 * 2 = 10. Let's find the cost of the french fries. We know that x sets of french fries cost 2.50 each, so the total cost of the french fries is 2.50 * x = 2.50x. The total bill is the sum of the cost of the Taco Salad, hamburgers, lemonade, and french fries: 10 + 25 + 10 + 2.50x. If they split the bill equally among the 5 friends, each friend will pay: (10 + 25 + 10 + 2.50x) / 5. We are given that each friend will pay 11, so we can write: (10 + 25 + 10 + 2.50x) / 5 = 11. Multiplying both sides by 5, we get: 10 + 25 + 10 + 2.50x = 55. Simplifying the left side, we get: 45 + 2.50x = 55. Subtracting 45 from both sides, we get: 2.50x = 10. Dividing both sides by 2.50, we get: x = 4. The value of x is 4. 4 The answer is: 4

question:To run his grocery store, Mr. Haj needs 4000 a day. This money is used to pay for orders done, delivery costs and employees' salaries. If he spends 2/5 of the total operation costs on employees' salary and 1/4 of the remaining amount on delivery costs, how much money does he pay for the orders done?

answer:Mr. Haj spends 2/5 of the total operation costs on employees' salaries, so he spends 2/5 x 4000 = 1600 on salaries. The remaining amount after paying salaries is 4000 - 1600 = 2400. Mr. Haj then spends 1/4 of the remaining amount on delivery costs, so he spends 1/4 x 2400 = 600 on delivery. The remaining amount after paying delivery costs is 2400 - 600 = 1800. Therefore, Mr. Haj pays 1800 for the orders done. 1800 The answer is: 1800