A student attempted to solve the word problem described below. Evaluate their method and explain the fundamental flaw in their reasoning. Why does their approach lead to an incorrect answer?

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Solving a word problem with chained relative quantities requires breaking it down into sequential steps. For example, to find the total number of beads for a project where Alice has twice as many as Bob, and Bob has five times as many as Charlie, the main question cannot be answered directly. It must first be decomposed into the prerequisite sub-questions: 'How many beads does Bob have?' and 'How many beads does Alice have?'. Answering these allows for the final calculation of the total.

Decomposing a Word Problem with Relative Quantities

This example demonstrates how to find a total when individual amounts are defined by chained relationships. Starting with the known fact that Charlie has 6 beads, we can calculate that Bob has five times this amount, resulting in 30 beads. Following this, Alice's quantity is determined to be twice Bob's, which is 60 beads. The total for their project is the sum of these individual amounts: 6 (Charlie) + 30 (Bob) + 60 (Alice) = 96 beads.

Example Calculation of a Total from Chained Relative Quantities

A team is building a tower with three types of blocks: red, blue, and green. They plan to use twice as many red blocks as blue blocks, and half as many blue blocks as green blocks. To find the total number of blocks needed if they start with 80 green blocks, which sequence of questions correctly breaks down the problem?

A baker is making a large batch of fruitcake. The recipe requires three times as much flour as sugar, and half as much sugar as raisins. Before calculating the total weight of these three ingredients, what two prerequisite questions must the baker answer first, assuming they know the weight of the raisins?

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