answer:To find the number of positive integers below 200 that are divisible by 2, 3, and 5, we need to find the positive integers that are divisible by the least common multiple (LCM) of these numbers, which is 60 (since 2, 3, and 5 have no common factors other than 1). First, let's determine how many multiples of 60 are present between 1 and 200. We can do this by dividing the larger number (200) by the LCM (60): Number of multiples = Larger number / LCM = 200 / 60 = 100/3 ≈ 33.33 Since there cannot be a fraction of a multiple, we round down to 33, indicating that there are 33 full sets of 60 multiples below 200. Next, we need to account for the possibility of some of these multiples being greater than 200. To ensure that all resulting multiples are below or equal to 200, we can use the expression: Below or equal to 200 = Larger number - {(Last multiple in the range - First multiple + 1) / LCM * LCM} First multiple = LCM = 60 Last multiple in the range = 200 Below or equal to 200 = 200 - {(200 - 60 + 1) / 60 * 60} = 200 - {141 / 60 * 60} = 200 - {4230/60} = 200 - 70.5 = 129.5 Again, we cannot have a fraction of a multiple, so we round down to 129, meaning that the largest multiple of 60 below or equal to 200 is 129. However, we must also consider the potential overlap between the multiples of 60 and the numbers divisible by both 2 and 3 (i.e., multiples of 6). The LCM of 2, 3, and 5 is 60, but if we only consider multiples of 60, we might miss numbers like 12 (which is divisible by both 2 and 3 but less than 60). To account for this, we can find the number of multiples of 6 below 200 and then subtract the number of multiples of 60 below 200: Multiples of 6 = Larger number / 6 = 200 / 6 = 33.33 Multiples of 60 = Larger number / 60 = 200 / 60 = 100/3 = 33.33 There are 33 multiples of 6, and 33 multiples of 60, so there is no overlap in this scenario. Therefore, there are 33 positive integers below 200 that are divisible by 2, 3, and 5.,To find the number of positive integers below 200 that are divisible by 2, 3, and 5, we need to find the least common multiple (LCM) of 2, 3, and 5. The LCM of 2, 3, and 5 is 30. To find the number of positive integers below 200 that are divisible by 30, we divide 200 by 30 and round down to the nearest whole number. 200/30 = 6.66666... Rounded down, we have 6. Therefore, there are 6 positive integers below 200 that are divisible by 2, 3, and 5. The answer is: 6,To find the number of positive integers below 200 that are divisible by 2, 3, and 5, we need to find the smallest common multiple of these numbers. The prime factorization of each number is: 2 = 2^1 3 = 3^1 5 = 5^1 The smallest common multiple of these numbers is the product of the highest powers of their prime factors, which is: 2^1 * 3^1 * 5^1 = 2 * 3 * 5 = 30 Since the smallest integer divisible by 2, 3, and 5 is 30, we need to find the number of positive integers less than or equal to 199 that are multiples of 30. To do this, we divide 199 by 30 and round to the nearest integer: 199 / 30 ≈ 6.633 Rounding to the nearest integer, we get: 6 Adding 1 to account for including a multiple of 30 less than or equal to 199, we find that there are 7 positive integers below 200 that are both divisible by 2, 3, and 5. However, there is a small mistake in the calculation. The correct calculation is: 199 / 30 = 6.633 (also round to the nearest integer, the result is 6) 199 - 30 * 6 = 9. Therefore, the total number is 1 fewer than previous (7-1=6).

answer:Edmund uses x inches of gift wrapper per gift box. He has 90 inches of gift wrapper per day. To find out how many gift boxes he can wrap every 3 days, we need to multiply the amount of gift wrapper per day by the number of days. So the total amount of gift wrapper used in 3 days is 90 * 3 = 270 inches. We can set up an equation to find the value of x: x * (number of gift boxes) = 270 We are given that the number of gift boxes is 15, so we can write: x * 15 = 270 Dividing both sides by 15, we get: x = 18 The value of x is 18. 18 The answer is: 18, If Edmund can wrap 15 gift boxes every 3 days with 90 inches of gift wrapper, then the number of gift boxes he can wrap per inch of gift wrapper is: 15 gift boxes / 90 inches = 1/6 gift box per inch of gift wrapper Therefore, x, the number of inches of gift wrapper Edmund uses per gift box, is equal to the reciprocal of the number of gift boxes he can wrap per inch of gift wrapper: x = 1 / (1/6 gift box per inch of gift wrapper) = 6 inches per gift box So, Edmund uses 6 inches of gift wrapper per gift box.,We can set up the equation as follows: Edmund has 90 inches of gift wrapper per day In 3 days, Edmund will have 90 inches/day * 3 days = 270 inches He can use 270 inches to wrap gift boxes Edmund uses x inches of gift wrapper per gift box If he can wrap 15 gift boxes, then 15 gift boxes * x inches = 270 inches We can divide both sides of the equation by x to solve for x: 15 * x / x = 270 / x 15 x^2 / x = 270 15 x = 270 x = 18 So the value of the unknown variable x is 18 inches of gift wrapper per gift box.

answer:To find the total capacity of all the tables, we first need to determine the seating capacity for each type of table: Capacity of rectangular tables seating 6 people = Number of tables * Seats per table = 4 tables * 6 seats = 24 seats Capacity of rectangular tables seating 4 people = Number of tables * Seats per table = 16 tables * 4 seats = 64 seats Capacity of round tables seating 10 people = Number of tables * Seats per table = 8 tables * 10 seats = 80 seats Now, let's add up the seating capacities of all three types of tables: Total capacity = Capacity of 6-seat tables + Capacity of 4-seat tables + Capacity of 10-seat tables = 24 seats + 64 seats + 80 seats = 168 seats The total capacity of all the tables at the party venue is 168 seats.,To find the total capacity of all the tables, you need to calculate the capacity of each type of table and then add them together. 4 tables that seat 6 people each = 4 * 6 = 24 people 16 tables that seat 4 people each = 16 * 4 = 64 people 8 round tables that seat 10 people each = 8 * 10 = 80 people Now, add the capacities of all the tables: Total capacity = 24 + 64 + 80 = 168 people So, the total capacity of all the tables at the party venue is 168 people.,The capacity of each table is given by the number of people it can seat. There are 4 tables that seat 6 people each, so the total capacity of these tables is 4 * 6 = 24 people. There are 16 tables that seat 4 people each, so the total capacity of these tables is 16 * 4 = 64 people. There are 8 round tables that seat 10 people each, so the total capacity of these tables is 8 * 10 = 80 people. To find the total capacity of all the tables, we add the capacities of each type of table: 24 + 64 + 80 = 168 people. 168 The answer is: 168

answer:To solve this problem, we need to determine the value of x, which represents the number of orange trees in Ahmed's orchard. Let's break down the information given: Number of apple trees in Hassan's orchard: 1 Number of orange trees in Hassan's orchard: 2 Number of apple trees in Ahmed's orchard: 4 * Number of apple trees in Hassan's orchard = 4 * 1 = 4 Number of orange trees in Ahmed's orchard: x Total number of trees in Hassan's orchard: Number of apple trees + Number of orange trees = 1 + 2 = 3 Total number of trees in Ahmed's orchard: Number of apple trees + Number of orange trees = 4 + x There are 9 more trees in Ahmed's orchard than in Hassan's orchard, so we can set up the equation: Total number of trees in Ahmed's orchard - Total number of trees in Hassan's orchard = 9 4 + x - 3 = 9 Let's simplify and solve for x: x + 1 = 9 To isolate x, we subtract 1 from both sides of the equation: x + 1 - 1 = 9 - 1 x = 8 The value of x is 8. 8 The answer is: 8, Let's break this down step by step: 1. We know that Hassan has one apple tree (a) and two orange trees (o). So, Hassan has a total of a + o = 1 + 2 = 3 trees. 2. The problem states that Ahmed has four times as many apple trees as Hassan. Since Hassan has one apple tree, Ahmed has 4 * 1 = 4 apple trees. 3. The problem also states that there are 9 more trees in Ahmed's orchard than in Hassan's. Therefore, Ahmed has 3 (Hassan's total) + 9 = 12 trees. 4. Since we already know that Ahmed has 4 apple trees, he must have 12 - 4 = 8 orange trees. So, Ahmed has 4 apple trees and 8 orange trees, making a total of 12 trees in his orchard.,Let's start by understanding the provided information: 1. Ahmed has x orange trees. 2. Ahmed has four times as many apple trees as Hassan, who has one apple tree. 3. Hassan has two orange trees. 4. There are 9 more trees in Ahmed's orchard than in Hassan's. Using this information, we can set up the following equations: a_Ahmed = 4 * a_Hassan a_Ahmed + o_Ahmed = a_Hassan + o_Hassan + 9 Where a_Ahmed and o_Ahmed represent the number of apple trees and orange trees owned by Ahmed respectively, and a_Hassan and o_Hassan represent the number of apple trees and orange trees owned by Hassan respectively. We know that a_Hassan = 1 and o_Hassan = 2. Substituting these values in the second equation, we get: a_Ahmed + o_Ahmed = (1 + 2) + 9 a_Ahmed + o_Ahmed = 12 We are trying to find the value of x, which represents the number of orange trees owned by Ahmed. To find the number of apple trees Ahmed has, we can use the first equation: a_Ahmed = 4 Now we can substitute these values back into the equation a_Ahmed + o_Ahmed = 12: 4 + o_Ahmed = 12 Now, we can subtract 4 from both sides of the equation: o_Ahmed = 12 - 4 o_Ahmed = 8 So, Ahmed has 8 orange trees.