3:5. How many girls and how many boys are in this school? There are \( r \) red marbles, \( b \) blue marbles and \( w \) white marbles in a bag. Write the ratio of the number of blue marbles to the total number of marbles in terms of \( r \), \( b \) and \( w \). The perimeter of a rectangle is equal to 280 meters. The ratio of its length to its width is \( 5: 2 \). Find the area of the rectangle.

Let's solve each part of your question step by step. ### Part 1: Ratio of Girls to Boys You mentioned a ratio of 3:5. This means that for every 3 girls, there are 5 boys. To find the total number of girls and boys, we can express them in terms of a variable \( x \): - Number of girls = \( 3x \) - Number of boys = \( 5x \) The total number of students in the school would be: \[ \text{Total} = 3x + 5x = 8x \] Without additional information about the total number of students, we cannot determine the exact number of girls and boys, but we can express them in terms of \( x \). ### Part 2: Ratio of Blue Marbles to Total Marbles You have \( r \) red marbles, \( b \) blue marbles, and \( w \) white marbles. The total number of marbles is: \[ \text{Total marbles} = r + b + w \] The ratio of the number of blue marbles to the total number of marbles is given by: \[ \text{Ratio of blue marbles} = \frac{b}{r + b + w} \] ### Part 3: Area of the Rectangle The perimeter of a rectangle is given by the formula: \[ \text{Perimeter} = 2(\text{Length} + \text{Width}) \] Given that the perimeter is 280 meters, we can set up the equation: \[ 2(L + W) = 280 \] Dividing both sides by 2 gives: \[ L + W = 140 \] You also mentioned that the ratio of the length to the width is \( 5:2 \). We can express the length and width in terms of a variable \( k \): - Length \( L = 5k \) - Width \( W = 2k \) Substituting these into the equation \( L + W = 140 \): \[ 5k + 2k = 140 \] This simplifies to: \[ 7k = 140 \] Dividing both sides by 7 gives: \[ k = 20 \] Now we can find the length and width: \[ L = 5k = 5 \times 20 = 100 \text{ meters} \] \[ W = 2k = 2 \times 20 = 40 \text{ meters} \] Finally, the area \( A \) of the rectangle is given by: \[ A = L \times W = 100 \times 40 = 4000 \text{ square meters} \] ### Summary of Answers 1. The number of girls and boys can be expressed as \( 3x \) and \( 5x \) respectively. 2. The ratio of blue marbles to total marbles is \( \frac{b}{r + b + w} \). 3. The area of the rectangle is \( 4000 \) square meters.