Appearance
question:Xanthia can read 100 pages per hour and Molly can read 50 pages per hour. If they each read the same book, and the book has 225 pages, how many more minutes than Xanthia would it take for Molly to finish reading the book?
answer:Xanthia can read 100 pages in 1 hour, so she can read frac{100}{60}=frac{5}{3} pages per minute. Molly can read 50 pages in 1 hour, so she can read frac{50}{60}=frac{5}{6} pages per minute. To find out how long it would take Molly to finish reading the book, we divide the total number of pages (225) by her reading speed (in pages per minute): frac{225}{frac{5}{6}}=225cdotfrac{6}{5}=270 minutes. To find out how many more minutes it would take for Molly to finish reading the book compared to Xanthia, we subtract the time it takes Xanthia to finish (225 pages divided by her reading speed): 270-frac{225}{frac{5}{3}}=270-frac{225cdot3}{5}=270-135=135 minutes. Therefore, it would take Molly 135 more minutes than Xanthia to finish reading the book.The answer is: 135
question:For what base-6 digit d is 2dd5_6 divisible by the base 10 number 11? (Here 2dd5_6 represents a base-6 number whose first digit is 2, whose last digit is 5, and whose middle two digits are both equal to d).
answer:We can rewrite 2dd5_6 as 2 cdot 6^3 + d cdot 6^2 + d cdot 6 + 5. Using the divisibility rule for 11, we have 2 cdot 6^3 + d cdot 6^2 + d cdot 6 + 5 equiv 2 + d - d + 5 equiv 7 pmod{11}. So, for 2dd5_6 to be divisible by 11, we must have 7 equiv 0 pmod{11}. The only digit d that satisfies this congruence is d = boxed{4}. The answer is: 4
question:Jenna wants to buy a concert ticket that costs x, plus five drink tickets for 7 each. If Jenna earns 18 an hour and works 30 hours a week, what percentage of her monthly salary will she spend on this outing? If we know the answer to the above question is 10, what is the value of unknown variable x?
answer:The cost of the concert ticket is x dollars. The cost of five drink tickets is 5 * 7 = 35. The total cost of the outing is the sum of the cost of the concert ticket and the cost of the drink tickets: x + 35. Jenna earns 18 an hour and works 30 hours a week, so her weekly salary is 18 * 30 = 540. Assuming there are 4 weeks in a month, Jenna's monthly salary is 540 * 4 = 2160. The percentage of her monthly salary that she will spend on this outing is: ((x + 35) / 2160) * 100. We are given that this percentage is 10, so we can write: ((x + 35) / 2160) * 100 = 10. Dividing both sides by 100, we get: (x + 35) / 2160 = 0.1. Multiplying both sides by 2160, we get: x + 35 = 216. Subtracting 35 from both sides, we get: x = 181. The value of x is 181. 181 The answer is: 181
question:After using 10 pounds of spicy meat mix to create a string of 40 sausage links, Brandy, the Golden Retriever, ate 12 links. How many ounces of sausage meat are left in the remaining links?
answer:If 10 pounds of spicy meat mix were used to create 40 sausage links, then each link contains 10/40 = 0.25 pounds of meat. Since there are 16 ounces in a pound, each link contains 0.25 * 16 = 4 ounces of meat. If Brandy ate 12 links, then the remaining links are 40 - 12 = 28. Therefore, there are 28 * 4 = 112 ounces of sausage meat left in the remaining links. 112 The answer is: 112