Two numbers have a sum of 25 and a difference of 13. Find their product:
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Answer: B. 114
Explanation
Setting up a system of linear equations with the given sum and difference determines both unknown numbers. Adding the two equations together eliminates one variable and reveals the first number as nineteen. Substituting the first number back into the equations gives the second number as six yielding their product. Systems of linear equations can be solved efficiently using the method of simultaneous addition. The product of two numbers is found by multiplying the individual numerical values together directly. Algebraic word problems translate descriptive sentences into mathematical equations for resolution.
Simultaneous equations are applied in economics to find market equilibrium prices and quantities. Basic algebra concepts like number relationships are foundational for advanced calculus and linear algebra. Financial accounting uses similar equation solving techniques to balance asset and liability ledgers. Option A suggests one hundred four which results from an arithmetic error during multiplication. Option C proposes three hundred fifteen which significantly overestimates the correct numerical product. Option D offers three25 which does not match the product of the derived number pair.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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