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question:Ashley has 3 siblings. The total weight of all 4 siblings combined is 560 pounds. One of her siblings weighs 140 pounds. Another sibling weighs 120 pounds. If Ashley weighs 10 pounds more than the last sibling, how much does Ashley weigh?
answer:First, I need to determine the total weight of all four siblings, which is 560 pounds.Two of the siblings weigh 140 pounds and 120 pounds respectively. Adding these together gives 260 pounds.Subtracting this from the total weight, the combined weight of Ashley and the last sibling is 560 - 260 = 300 pounds.Let’s denote the weight of the last sibling as x. Since Ashley weighs 10 pounds more than this sibling, her weight is x + 10 pounds.Together, Ashley and the last sibling weigh x + (x + 10) = 2x + 10 pounds, which equals 300 pounds.Solving for x: 2x + 10 = 300 → 2x = 290 → x = 145 pounds.Therefore, Ashley weighs 145 + 10 = 155 pounds.
question:In a small farm, there are 120 ducks. A quarter of the ducks are white, and 30 percent of the white ducks are female. How many more white male ducks are there than white female ducks?
answer:First, I need to determine the total number of white ducks on the farm. Since a quarter of the 120 ducks are white, I calculate 120 divided by 4, which equals 30 white ducks.Next, I'll find out how many of these white ducks are female. Given that 30% of the white ducks are female, I multiply 30 by 0.30, resulting in 9 female white ducks.To find the number of male white ducks, I subtract the number of female white ducks from the total number of white ducks. So, 30 minus 9 equals 21 male white ducks.Finally, to determine how many more male white ducks there are than female white ducks, I subtract the number of female white ducks from the number of male white ducks. This gives me 21 minus 9, which equals 12 more male white ducks.
question:There are 4 ships that have 30 crates. There are 6 ships that have 18 crates. Each crate holds 6 barrels of juice. If all of the juice is evenly redistributed onto 8 ships, how many barrels of juice will each ship have?
answer:First, I need to calculate the total number of crates from both groups of ships. There are 4 ships with 30 crates each and 6 ships with 18 crates each.Next, I'll determine the total number of barrels of juice by multiplying the total number of crates by the number of barrels each crate holds, which is 6.After finding the total barrels, I'll redistribute this amount evenly across the 8 ships by dividing the total barrels by 8.This will give me the number of barrels each ship will have after redistribution.
question:A social media platform has 400 active users. The average number of comments posted by each user is twice as many as the number of posts shared. If each user shares an average of 2 posts per hour, calculate the total number of posts and comments made on the platform by its users in a 12-hour period.
answer:First, I need to determine the average number of comments each user posts. Since the number of comments is twice the number of posts, and each user shares 2 posts per hour, the average comments per user per hour would be 2 times 2, which equals 4 comments.Next, I'll calculate the total number of posts made by all users in 12 hours. With 400 active users each sharing 2 posts per hour, the total posts per hour are 400 multiplied by 2, resulting in 800 posts per hour. Over 12 hours, this amounts to 800 multiplied by 12, totaling 9,600 posts.Similarly, I'll calculate the total number of comments. Each user posts 4 comments per hour, so for 400 users, the total comments per hour are 400 multiplied by 4, which is 1,600 comments per hour. Over 12 hours, this becomes 1,600 multiplied by 12, resulting in 19,200 comments.Finally, to find the total number of posts and comments combined, I'll add the total posts and total comments together: 9,600 posts plus 19,200 comments equals 28,800 total posts and comments.
question:George collected 50 marbles in white, yellow, green, and red. Half of them are white, and 12 are yellow. There are 50% fewer green balls than yellow balls. How many marbles are red?
answer:First, I note that George has a total of 50 marbles, which are white, yellow, green, and red.Half of the marbles are white, so there are 25 white marbles.There are 12 yellow marbles.The number of green marbles is 50% fewer than the number of yellow marbles. To find this, I calculate 50% of 12, which is 6, and subtract that from 12, resulting in 6 green marbles.Finally, to find the number of red marbles, I subtract the total number of white, yellow, and green marbles from the overall total: 50 - 25 - 12 - 6 = 7 red marbles.
question:Class 4A used the class fund to buy three types of stationery with unit prices of 3 yuan, 2 yuan, and 1 yuan respectively. It is known that the number of Type B stationery purchased is 2 less than the number of Type A stationery purchased, and the cost of Type A stationery does not exceed half of the total cost. If the total expenditure for the three types of stationery is exactly 66 yuan, what is the maximum number of Type A stationery purchased?
answer:Alright, let's tackle this problem step by step. So, we have three types of stationery: Type A, Type B, and Type C, with unit prices of 3 yuan, 2 yuan, and 1 yuan respectively. The class fund spent exactly 66 yuan on these. First, let's note down the given information:1. The number of Type B stationery purchased is 2 less than the number of Type A. So, if we let the number of Type A be ( x ), then Type B is ( x - 2 ).2. The cost of Type A stationery does not exceed half of the total cost. Since the total expenditure is 66 yuan, half of that is 33 yuan. So, the cost for Type A, which is ( 3x ), must be less than or equal to 33 yuan. That gives us the inequality ( 3x leq 33 ), which simplifies to ( x leq 11 ). So, the maximum possible number of Type A stationery is 11, but we need to check if this is feasible given the other constraints.3. The total expenditure is 66 yuan. So, the sum of the costs for Type A, B, and C should be 66.Let's denote:- ( x ) = number of Type A stationery- ( y ) = number of Type B stationery = ( x - 2 )- ( z ) = number of Type C stationerySo, the total cost equation is:[ 3x + 2y + z = 66 ]But since ( y = x - 2 ), we can substitute that in:[ 3x + 2(x - 2) + z = 66 ]Simplify:[ 3x + 2x - 4 + z = 66 ]Combine like terms:[ 5x - 4 + z = 66 ]Then:[ 5x + z = 70 ]So, ( z = 70 - 5x )Now, since the number of stationery can't be negative, ( z geq 0 ). Therefore:[ 70 - 5x geq 0 ][ 5x leq 70 ][ x leq 14 ]But earlier, we had ( x leq 11 ) from the cost constraint. So, the maximum possible ( x ) is 11, but we need to ensure that ( z ) is a non-negative integer.Let's check if ( x = 11 ) works:- ( y = 11 - 2 = 9 )- ( z = 70 - 5*11 = 70 - 55 = 15 )So, ( z = 15 ), which is non-negative. So, ( x = 11 ) is possible.Wait, but let's verify the total cost:- Type A: 11 * 3 = 33- Type B: 9 * 2 = 18- Type C: 15 * 1 = 15Total: 33 + 18 + 15 = 66, which matches.But wait, the cost of Type A is exactly half of the total cost (33 yuan out of 66). The problem states that the cost of Type A does not exceed half, so 33 is acceptable.But let's check if a higher ( x ) is possible, but from the earlier constraint, ( x leq 11 ). So, 11 is the maximum.Wait, but let me double-check. If ( x = 12 ), then ( y = 10 ), and ( z = 70 - 60 = 10 ). But the cost for Type A would be 12*3=36, which is more than 33, violating the condition that Type A's cost does not exceed half of the total cost. So, 12 is not allowed.Therefore, the maximum number of Type A stationery is 11.Wait, but let me check if there's a higher ( x ) that still keeps the cost under or equal to 33. Since 3x ≤33, x ≤11, so 11 is indeed the maximum.But just to be thorough, let's see if ( x =11 ) is the only solution or if there are other values. For example, ( x =10 ), then ( y=8 ), ( z=70-50=20 ). Total cost: 30+16+20=66. That works too, but since we're looking for the maximum, 11 is better.So, the answer should be 11.