answer:The value of x is 6. Here's the logic behind this: 1. Let's first find the meowing frequency ratio of the three cats: Cat 1 (C1) - x times per minute, Cat 2 (C2) - 2x times per minute, and Cat 3 (C3) - (2x/3) times per minute. 2. Now we need to find a relationship between their frequencies so that their combined total in 5 minutes equals 55. To do this, let's add up their individual frequencies and multiply by 5: (5x) + (10x) + (10x/3) = 55 3. To solve for x, first multiply all terms by 3 to eliminate the fraction: 15x + 30x + 10x = 165 4. Combine like terms: 55x = 165 5. Divide both sides by 55: x = 3 However, upon further examination, using x=3 would result in whole numbers for only two cats (C1 and C2), while making C3 a fraction. Since it's stated that each cat's frequency is a whole number, we need to test other values of x to find a whole-number solution. If we try x=6, then C1 meows 6 times per minute, C2 meows 12 times per minute (twice as frequent), and C3 meows 4 times per minute (one-third the frequency of C2). This satisfies the conditions of the problem: C1 + C2 + C3 = 6 + 12 + 4 = 22 meows per minute 22 meows per minute * 5 minutes = 110 meows in 5 minutes But the problem states that the total number of meows in 5 minutes is 55. Since we have double the required number of meows, we can assume that our time frame is also doubled. Therefore, reducing all frequencies by half will give us the correct answer: C1 meows 3 times per minute, C2 meows 6 times per minute (twice as frequent), and C3 meows 2 times per minute (one-third the frequency of C2). C1 + C2 + C3 = 3 + 6 + 2 = 11 meows per minute 11 meows per minute * 5 minutes = 55 meows in 5 minutes Thus, the value of x is 6.,To solve this problem, we need to determine the value of x, which represents the number of times the first cat meowed per minute. Let's break down the information given: Number of times the first cat meowed per minute: x Number of times the second cat meowed per minute: 2x (twice as frequently as the first cat) Number of times the third cat meowed per minute: (1/3) * 2x (one-third the frequency of the second cat) Total number of meows in 5 minutes: 55 We can set up the equation as follows: Number of times the first cat meowed per minute * 5 + Number of times the second cat meowed per minute * 5 + Number of times the third cat meowed per minute * 5 = Total number of meows in 5 minutes 5x + 5 * 2x + 5 * (1/3) * 2x = 55 Let's simplify and solve for x: 5x + 10x + (10/3)x = 55 To combine the terms with x, we find a common denominator of 3: (15/3)x + (30/3)x + (10/3)x = 55 (55/3)x = 55 To isolate x, we divide both sides of the equation by 55/3: (55/3)x / (55/3) = 55 / (55/3) x = 3 The value of x is 3. 3 The answer is: 3,To solve this problem, let's break it down into parts: 1. First cat meows x times per minute. 2. Second cat meows twice as often as the first cat, so it meows 2x times per minute. 3. Third cat meows at one-third the frequency of the second cat, so it meows x/3 times per minute. We're given that the combined total number of meows the three cats make in 5 minutes is 55. Therefore, we have the equation: 5(x + 2x + x/3) = 55 Let's simplify and solve for x: 5(6x/3) = 55 10x = 55 x = 5.5 So, the value of x is 5.5 meows per minute.

answer:First, let's find out how many red bouncy balls Kate bought: Red bouncy balls = Number of packs * Balls per pack = 7 packs * 18 balls = 126 balls Next, let's find out how many yellow bouncy balls Kate bought: Yellow bouncy balls = Number of packs * Balls per pack = 6 packs * 18 balls = 108 balls Now, to find the difference between the number of red and yellow bouncy balls, we subtract the number of yellow balls from the number of red balls: Difference = Red bouncy balls - Yellow bouncy balls = 126 balls - 108 balls = 18 balls So, Kate bought 18 more red bouncy balls than yellow bouncy balls.,Kate bought 7 packs of red bouncy balls, so she bought a total of 7 * 18 = 126 red bouncy balls. She also bought 6 packs of yellow bouncy balls, so she bought a total of 6 * 18 = 108 yellow bouncy balls. To find the difference in the number of red and yellow bouncy balls, we subtract the number of yellow bouncy balls from the number of red bouncy balls: 126 - 108 = 18. Kate bought 18 more red bouncy balls than yellow bouncy balls. 18 The answer is: 18,Kate bought 7 packs of red bouncy balls which is a total of 7 * 18 = 126 red bouncy balls. She also bought 6 packs of yellow bouncy balls which is a total of 6 * 18 = 108 yellow bouncy balls. To find out how many more red bouncy balls she bought than yellow ones, subtract the total number of yellow bouncy balls from the total number of red bouncy balls. So Kate bought 126 - 108 = 18 more red bouncy balls than yellow ones.

answer:The first 5 students turned in essays with a total of 5 * 2 = 10 pages. The next 5 students turned in essays with a total of 5 * 3 = 15 pages. The last 5 students turned in essays with a total of 5 * 1 = 5 pages. In total, the 15 students turned in essays with 10 + 15 + 5 = 30 pages. The average page count per essay is 30 / 15 = 2 pages. 2 The answer is: 2,To find the average page count per essay for the 15 students, we need to calculate the total number of pages and divide it by the total number of students. Total pages from the first 5 students each with 2 pages = 5 * 2 = 10 pages Total pages from the next 5 students each with 3 pages = 5 * 3 = 15 pages Total pages from the last 5 students each with 1 page = 5 * 1 = 5 pages Total pages for all 15 students = 10 + 15 + 5 = 30 pages Now, we divide the total pages by the total number of students: Average page count per essay = Total pages / Total students = 30 pages / 15 students = 2 pages The average page count per essay for the 15 students is 2 pages., To find the average page count per essay, we first need to determine the total number of pages turned in by all 15 students: Total pages = (Pages from first 5 students * Number of students) + (Pages from next 5 students * Number of students) + (Pages from last 5 students * Number of students) Total pages = (2 * 5) + (3 * 5) + (1 * 5) Total pages = 10 + 15 + 5 Now, calculate the total pages: Total pages = 30 Next, divide the total number of pages by the number of students to find the average page count per essay: Average page count = Total pages / Number of students Average page count = 30 / 15 So, Average page count = 2 The average page count per essay for the 15 students is 2 pages.

answer:On that particular day, Matthew spent 1 hour gathering ingredients, 1 hour gathering ingredients, 1.5 hours baking the cakes, but due to the oven malfunction, it took 1.5 hours x 2 = 3 hours to bake the cakes. And since he only had to decorate one cake, it took him 1 more hour. So, on that day, it took Matthew a total of 1 hour (ingredients) + 1 hour (oven failure) + 3 hours (baking) + 1 hour (decoration) = 6 hours to make his famous caramel-apple coffee cakes., It took Matthew 5 hours to make his famous caramel-apple coffee cakes on that day. Here's the reasoning: 1. Gathering ingredients still takes 1 hour. 2. Baking the cakes now takes twice as long, so 1.5 hours * 2 = 3 hours. 3. Decorating each cake with cinnamon sprinkles still takes 1 hour. 4. To find the total time, we add up the time for each step: 1 hour (gathering) + 3 hours (baking) + 1 hour (decorating) = 5 hours.,On a regular day, it takes Matthew 1 hour to gather ingredients, 1.5 hours to bake the cakes, and 1 hour to decorate each cake. So, on a regular day, it takes Matthew a total of 1 + 1.5 + 1 = 3.5 hours to make each cake. However, on that particular day, the cakes took twice as long to bake, so it took Matthew 1.5 * 2 = 3 hours to bake each cake. Therefore, on that day, it took Matthew a total of 1 + 3 + 1 = 5 hours to make each cake. 5 The answer is: 5