28% of the people at an opening ceremony were men. The number of the men was 220 fewer than the number of women and children. The ratio of the number of women to the number of children was 2:1. How...

Let's start by using algebra to represent the information given in the problem. Let's say that the total number of people at the opening ceremony is "x". Then, we know that 28% of them were men, so the number of men can be represented as 0.28x. We also know that the number of men was 220 fewer than the number of women and children. Let's say that the number of women and children is "y". Then, we can set up an equation: 0.28x = y - 220 Finally, we know that the ratio of women to children is 2:1. Let's say that the number of children is "c". Then, we can set up another equation: y = 2c Now we have two equations with two variables (y and c). We can substitute the second equation into the first equation to eliminate y: 0.28x = 2c - 220 Simplifying this equation: 0.14x + 110 = c So we now know that the number of children is 0.14 times the total number of people, plus 110. We can substitute this expression for c into the equation y = 2c to get: y = 2(0.14x + 110) Simplifying: y = 0.28x + 220 Now we have two equations with two variables (y and x). We can substitute the second equation into the equation for the percentage of men to get: 0.28x = (0.28x + 220) - 220 Simplifying: 0.28x = 0.28x This is true for any value of x, which means that our equations are consistent and we can solve for c. Using the equation we found earlier: c = 0.14x + 110 We know that c is a whole number, so we need to find a value of x that makes c a whole number. Let's try some values: If x = 1000, then c = 240, which works because 240 is a multiple of 1 (the ratio of women to children is 2:1). Therefore, there were 240 children at the opening ceremony.