answer:Let's denote Hansol's weight as H kg. Since Hanbyul is 4 kg heavier than Hansol, Hanbyul's weight would be H + 4 kg. According to the information given, the total weight of Hanbyul and Hansol is 88 kg. So we can write the equation: H (Hansol's weight) + (H + 4) (Hanbyul's weight) = 88 kg Now, let's solve for H: H + H + 4 = 88 2H + 4 = 88 2H = 88 - 4 2H = 84 H = 84 / 2 H = 42 So, Hansol weighs boxed{42} kg.

answer:** 1. **Set up the equation from the given ratio:** The problem gives the ratio of 3x^2-y to x+y as frac{1}{2}, written as: [ frac{3x^2 - y}{x + y} = frac{1}{2}. ] 2. **Cross-multiply to eliminate the fraction:** Following the setup, we cross-multiply: [ 2(3x^2 - y) = 1(x + y). ] Expanding both sides gives: [ 6x^2 - 2y = x + y. ] 3. **Simplify and rearrange the equation:** Group the x and y terms to simplify: [ 6x^2 - x = 3y. ] Dividing by 3, we get an expression for y in terms of x: [ y = frac{6x^2 - x}{3}. ] 4. **Expressing the ratio frac{x}{y}:** Substitute y: [ frac{x}{y} = frac{x}{frac{6x^2 - x}{3}} = frac{3x}{6x^2 - x}. ] Simplifying the expression: [ frac{x}{y} = frac{3}{6x - 1}. ] 5. **Conclusion and boxed answer:** The ratio of x to y, as derived, is: [ frac{3{6x-1}}. ] This expression provides the ratio in terms of x and depends on the value of x. ** The final answer is ** boxed{text{(B)} frac{3}{6x-1}} is the correct answer. **

answer:First, let's find out how many peaches Susan bought in total. Since a dozen is 12, five dozen peaches would be: 5 dozen * 12 peaches/dozen = 60 peaches Susan placed 12 peaches in the knapsack, so the remaining peaches to be placed in the cloth bags would be: 60 peaches - 12 peaches = 48 peaches Since the two cloth bags are identically-sized, she would divide the remaining peaches equally between them: 48 peaches / 2 bags = 24 peaches per bag Now, to find the ratio of the number of peaches in the knapsack to the number of peaches in each cloth bag, we compare the number of peaches in the knapsack (12) to the number of peaches in one cloth bag (24): Ratio = number of peaches in knapsack : number of peaches in one cloth bag Ratio = 12 : 24 To simplify the ratio, we divide both numbers by the greatest common divisor, which is 12: Ratio = (12/12) : (24/12) Ratio = 1 : 2 So, the ratio of the number of peaches in the knapsack to the number of peaches in each cloth bag is boxed{1:2} .

answer:To solve this problem, we need to divide the set {2, 3, cdots, 9} into 4 pairs such that no pair of numbers has a greatest common divisor (gcd) equal to 2. This means that no pair can consist of two even numbers. 1. **Identify the even and odd numbers:** The set {2, 3, 4, 5, 6, 7, 8, 9} contains four even numbers {2, 4, 6, 8} and four odd numbers {3, 5, 7, 9}. 2. **Pair each even number with an odd number:** Since we cannot pair two even numbers together, each even number must be paired with an odd number. We need to count the number of ways to pair the four even numbers with the four odd numbers. 3. **Calculate the number of bijections:** The number of ways to pair four even numbers with four odd numbers is the number of bijections (one-to-one correspondences) between the two sets. This is given by the number of permutations of the four odd numbers, which is 4! (4 factorial). [ 4! = 4 times 3 times 2 times 1 = 24 ] 4. **Consider the special case where 4 and 8 are paired together:** We can also pair 4 and 8 together, while pairing 2 and 6 with odd numbers. We need to count the number of ways to pair 2 and 6 with two elements of the set {3, 5, 7, 9}. - First, choose 2 odd numbers out of 4 to pair with 2 and 6. The number of ways to choose 2 odd numbers out of 4 is given by the binomial coefficient binom{4}{2}. [ binom{4}{2} = frac{4!}{2!(4-2)!} = frac{4 times 3}{2 times 1} = 6 ] - Next, pair the chosen odd numbers with 2 and 6. There are 2! ways to pair 2 and 6 with the chosen odd numbers. [ 2! = 2 times 1 = 2 ] - Therefore, the total number of ways to pair 2 and 6 with two odd numbers is: [ 6 times 2 = 12 ] 5. **Combine the results:** We have 24 ways to pair each even number with an odd number, and 12 ways to pair 4 and 8 together while pairing 2 and 6 with odd numbers. Therefore, the total number of ways to divide the set into 4 pairs such that no pair has gcd equal to 2 is: [ 24 + 12 = 36 ] The final answer is boxed{36}.