answer:To solve this problem, we need to determine the value of x, which represents the number of times Joe has as many marshmallows as his dad. Let's break down the information given: Number of marshmallows Joe's dad has: 21 Number of marshmallows Joe has: x * 21 Joe's dad roasts a third of his marshmallows: (1/3) * 21 Joe roasts half of his marshmallows: (1/2) * (x * 21) Total number of marshmallows roasted: 49 We can set up the equation as follows: Number of marshmallows Joe's dad roasts + Number of marshmallows Joe roasts = Total number of marshmallows roasted (1/3) * 21 + (1/2) * (x * 21) = 49 Let's simplify and solve for x: 7 + (1/2) * (x * 21) = 49 To get rid of the fraction, we multiply both sides of the equation by 2: 14 + x * 21 = 98 To isolate x, we subtract 14 from both sides of the equation and divide by 21: 14 + x * 21 - 14 = 98 - 14 x * 21 = 84 x = 84 / 21 x = 4 The value of x is 4. 4 The answer is: 4, The value of x is 7. Here's the reasoning: 1. Joe's dad has 21 marshmallows. 2. Joe has x times as much marshmallows as his dad, so Joe has 21x marshmallows. 3. Joe's dad roasts a third of his marshmallows, which is 21 * (1/3) = 7 marshmallows. 4. Joe roasts half of his marshmallows, which is 21x * 0.5 = 10.5x marshmallows. 5. Together, they roast 7 + 10.5x marshmallows, which equals 49 marshmallows in total. 6. So, 7 + 10.5x = 49 7. To find the value of x, we first subtract 7 from both sides of the equation: 10.5x = 42 8. Then, we divide by 10.5 to solve for x: x = 42 / 10.5 = 4 9. However, since Joe must have an integer number of marshmallows (as it's not possible to have a fraction of a marshmallow), there was a mistake in the calculation. It should be x = 21x * 0.5 = 42 instead of 10.5x. 10. So, x = 42 / 2 = 7.,Let's break this down step by step: 1. Joe's dad has 21 marshmallows and roasts 1/3 of them. So he roasted 21 * 1/3 = 7 marshmallows. 2. Joe has x times as much marshmallows as his dad, which means Joe has x * 21 marshmallows. 3. Joe roasts 1/2 of his marshmallows, so he roasted (1/2) * (x * 21) = x * 21 * 1/2 = 10.5x marshmallows. 4. In total, they roasted 7 + 10.5x marshmallows. But we know they roasted 49 marshmallows, so we can set up an equation: 7 + 10.5x = 49 5. Now, let's solve for x: 10.5x = 42 x = 42 / 10.5 x = 4 Therefore, the value of x is 4. Joe has 4 times as many marshmallows as his dad.

answer:If there are 12 slices in a pizza, then half of a pizza is 12/2 = 6 slices. One-third of a pizza is 12/3 = 4 slices. One-sixth of a pizza is 12/6 = 2 slices. A quarter of a pizza is 12/4 = 3 slices. In total, they ate 6 + 4 + 2 + 3 = 15 slices. If they had 2 pizzas, then there were 2 x 12 = 24 slices in total. Therefore, there were 24 - 15 = 9 slices left after they finished eating. 9 The answer is: 9,Let's first find out how many slices each person ate: Bob ate 1/2 of a pizza, and since each pizza has 12 slices, Bob ate 1/2 * 12 = 6 slices. Tom ate 1/3 of a pizza, so Tom ate 1/3 * 12 = 4 slices. Sally ate 1/6 of a pizza, so Sally ate 1/6 * 12 = 2 slices. Jerry ate 1/4 of a pizza, so Jerry ate 1/4 * 12 = 3 slices. Now we can add up the number of slices they ate: 6 + 4 + 2 + 3 = 15 slices. Initially, they had 2 pizzas, and each pizza has 12 slices, so they started with 2 * 12 = 24 slices. After eating their share, they had 24 - 15 = 9 slices left., There were 3 slices left. Here's the reasoning: 1. Bob ate half of a pizza, which is 12 slices / 2 = 6 slices. 2. Tom ate one-third of a pizza, which is 12 slices / 3 = 4 slices. 3. Sally ate one-sixth of a pizza, which is 12 slices / 6 = 2 slices. 4. Jerry ate a quarter of a pizza, which is 12 slices / 4 = 3 slices. 5. In total, they ate 6 slices (Bob) + 4 slices (Tom) + 2 slices (Sally) + 3 slices (Jerry) = 15 slices. 6. Each pizza has 12 slices, so two pizzas have a total of 24 slices. 7. After eating 15 slices, there are 24 slices - 15 slices = 9 slices left. However, the question asks for the number of "full" slices left, not the total number of leftover pieces (which could include fractional slices). Since the pizza was evenly divided into 12 equal slices, any leftover piece must also be a full slice. Therefore, we need to check if there are any fractional slices remaining: 8. The total number of eaten slices, when rounded up to the nearest multiple of 12, is 18 slices (since 15 slices are just 3 short of 18). 9. So, there are actually 24 - 18 = 6 full slices eaten, leaving 24 - 6 = 18 full slices intact. 10. But the question states that they ate 15 slices, which should mean that there are 24 - 15 = 9 full slices left. However, we know this isn't true because we rounded up the eaten slices to 18. 11. To correct for this, we must add back the 3 extra slices we included in our eaten total: 15 eaten slices + 3 extra slices = 18 slices. 12. Subtracting this from the original 24 slices, we find that there are 24 - 18 = 3 full slices left.

answer:The number of students who want to go on a skiing trip is twice as many as the number of students who want to go on a scavenger hunting trip, so it is 2 * 4000 = 8000 students. The total number of students who want to go on either trip is 4000 + 8000 = 12000 students. 12000 The answer is: 12000, To find the number of students who want to go on a skiing trip, we can take the number of students who want to go on the scavenger hunting trip (4000) and multiply it by 2 (since there are twice as many students who want to go skiing): 4000 * 2 = 8000 students To find the total number of students who want to go on either the scavenger hunting trip or the skiing trip, we can add the number of students who want to go on each trip: Total students = students who want to go on scavenger hunt + students who want to go on skiing trip = 4000 + 8000 = 12,000 students Therefore, there are a total of 12,000 students who want to go on either the scavenger hunting trip or the skiing trip.,If the number of students who want to go on a skiing trip is twice as many as the number of students who want to go on the scavenger hunting trip, we can calculate the total number of students as follows: 4000 (scavenger hunting trip) + 4000 x 2 (skiing trip) = 4000 + 8000 = 12,000 So, the total number of students altogether is 12,000.

answer:Let's analyze the information given: 1. There were 100 people in total at the party. 2. Fifty percent of them are women, so there were 0.5 * 100 = 50 women. 3. Thirty-five percent of them are men, so there were 0.35 * 100 = 35 men. Now, let's find out how many children attended the party: 1. We know that there were 50 women and 35 men, which adds up to 85 people with known genders. 2. Since there were 100 people in total, this means that there must be 100 - 85 = 15 people who are not classified as women or men. 3. Therefore, there were 15 children who attended the party. The final answer is that 15 children attended the party.,Since the percentages add up to 100%, the rest of the attendees (which would be the children) account for: 100% - 50% (women) - 35% (men) = 15% There were 100 people in total, so to find the number of children, we can multiply the total number of people by 15%: 100 people * 15% = 15 children So, 15 children attended the party.,50% of the attendees are women, so there are 100 x 0.50 = 50 women. 35% of the attendees are men, so there are 100 x 0.35 = 35 men. The remaining attendees are children, so there are 100 - 50 - 35 = 15 children. Therefore, 15 children attended the party. 15 The answer is: 15