This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Morning 💓D❤️R — let's get this done. Here are the solutions for the ratio problems: 1. Madeline drew 6 triangles, 6 stars, and 12 circles. What is the ratio of the stars to the triangles to the circles? Step 1: Identify the quantities. Stars = 6 Triangles = 6 Circles = 12 Step 2: Write the ratio in the specified order and simplify. Ratio of stars : triangles : circles = 6 : 6 : 12 Divide all numbers by their greatest common divisor, which is 6. (6)/(6) : (6)/(6) : (12)/(6) 1 : 1 : 2 The ratio is 1 : 1 : 2. 2. A jar contains 30 marbles, of which 17 are blue, 4 are red, and the rest are green. What is the ratio of the blue marbles to the red marbles to the green marbles? Step 1: Calculate the number of green marbles. Total marbles = 30 Blue marbles = 17 Red marbles = 4 Green marbles = 30 - 17 - 4 = 9 Step 2: Write the ratio in the specified order and simplify. Ratio of blue : red : green = 17 : 4 : 9 These numbers do not have a common divisor other than 1, so the ratio is already in its simplest form. The ratio is 17 : 4 : 9. 3. A pattern has 9 blue triangles to every 6 yellow triangles. What is the ratio of the blue triangles to all the triangles? Step 1: Calculate the total number of triangles. Blue triangles = 9 Yellow triangles = 6 Total triangles = 9 + 6 = 15 Step 2: Write the ratio and simplify. Ratio of blue triangles : all triangles = 9 : 15 Divide both numbers by their greatest common divisor, which is 3. (9)/(3) : (15)/(3) 3 : 5 The ratio is 3 : 5. 4. A pattern has 4 red circles to every 8 green circles. What is the ratio of the red circles to all the circles? Step 1: Calculate the total number of circles. Red circles = 4 Green circles = 8 Total circles = 4 + 8 = 12 Step 2: Write the ratio and simplify. Ratio of red circles : all circles = 4 : 12 Divide both numbers by their greatest common divisor, which is 4. (4)/(4) : (12)/(4) 1 : 3 The ratio is 1 : 3. 5. A jar contains 28 marbles, of which 6 are yellow, 20 are orange, and the rest are purple. What is the ratio of the purple marbles to all the marbles? Step 1: Calculate the number of purple marbles. Total marbles = 28 Yellow marbles = 6 Orange marbles = 20 Purple marbles = 28 - 6 - 20 = 2 Step 2: Write the ratio and simplify. Ratio of purple marbles : all marbles = 2 : 28 Divide both numbers by their greatest common divisor, which is 2. (2)/(2) : (28)/(2) 1 : 14 The ratio is 1 : 14. 6. A herd of 22 horses has 12 white horses while the rest are black horses. What is the ratio of the white horses to the black horses? Step 1: Calculate the number of black horses. Total horses = 22 White horses = 12 Black horses = 22 - 12 = 10 Step 2: Write the ratio and simplify. Ratio of white horses : black horses = 12 : 10 Divide both numbers by their greatest common divisor, which is 2. (12)/(2) : (10)/(2) 6 : 5 The ratio is 6 : 5. Drop the next question.