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
You're on a roll — Step 1: Combine the given ratios x:y = 1:2 and y:z = 1:3. To combine these ratios, we need to make the value for y consistent. The ratio x:y = 1:2 means for every 1 part of x, there are 2 parts of y. The ratio y:z = 1:3 means for every 1 part of y, there are 3 parts of z. To make y consistent, we can multiply the second ratio by 2: y:z = (1 × 2) : (3 × 2) = 2:6. Now we have x:y = 1:2 and y:z = 2:6. So, the combined ratio is x:y:z = 1:2:6. Step 2: Represent the number of marbles using a common multiplier. Let the common multiplier be k. Number of x marbles = 1k Number of y marbles = 2k Number of z marbles = 6k Step 3: Use the total number of marbles to find the value of k. The total number of marbles is 27. 1k + 2k + 6k = 27 9k = 27 k = (27)/(9) k = 3 Step 4: Calculate the number of z marbles. The number of z marbles is 6k. Number of z marbles = 6 × 3 = 18. The number of z marbles in the bag is 18. Drop the next question.