Math Problem Statement
Four friends, Alice, Bob, Charlie, and Diana, went to a store to buy some items. Each of them
bought different types of items: books, notebooks, erasers, and pencils. Exactly one of them
purchased books, exactly two of them purchased notebooks, exactly three of them purchased erasers, and all of them purchased pencils.
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The total number of books purchased was half of the number of erasers that Alice purchased.
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The total number of notebooks purchased was the same as the total number of items that Diana purchased.
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The number of pencils that Charlie purchased was the same as the number of erasers that Diana purchased.
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The total number of erasers purchased was 10 more than the total number of notebooks purchased, which was 20 more than the total number of pencils purchased.
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Alice, Bob, and Charlie purchased three notebooks, four erasers, and five pencils respectively (along with other items they may have purchased).If the number of total items with Diana is 48 more than the number of total items with Charlie, find the total number of items purchased by these four persons.
Solution
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Math Problem Analysis
Mathematical Concepts
Algebra
Equations
Problem Solving
Formulas
Equations involving multiple variables
Theorems
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Suitable Grade Level
Grades 9-12
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