16 pens and 8 pencils cost Rs. 352, while 4 pens and 4 pencils cost Rs. 96. Find the price of a single pen.
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Answer: E. None of these
Explanation
Dividing the second equation by four gives the simplified sum that one pen plus one pencil costs twenty four. Simplifying the first equation yields two pens plus one pencil costing forty four. Subtracting the two simplified equations reveals that a single pen costs twenty, making option E correct. Simultaneous linear equations allow finding individual item costs from multiple bundled purchase totals. Systematic elimination helps isolate a single variable by removing common terms between equations. Multiple choice tests include a none of the above option when the correct numeric value is missing from the list.
Retailers use cost analysis equations to determine profit margins on individual inventory items. Budgeting exercises often require solving simultaneous equations to find unit prices of mixed goods. Algebraic reasoning skills developed through these problems apply directly to advanced economic modeling. Option A is incorrect because the true price of a single pen derived from the equations is twenty. Option B overestimates the price of an individual pen based on faulty subtraction. Option C suggests a pen price that fails to satisfy both original purchase cost equations.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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