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Two shelves hold the same number of books. The first has 4 equal stacks and 7 loose books; the second has 6 stacks of that same size and 1 loose book. How many books are in one stack?

Class 7Simple EquationsSimple Equations
  • A3
  • B4
  • C6
  • D19

Step-by-Step Solution

Let a stack hold s books. Equal shelves give 4s + 7 = 6s + 1 → 7 − 1 = 6s − 4s → 6 = 2s → s = 3. Check: 4(3) + 7 = 19 and 6(3) + 1 = 19 ✓. Answer 4 adds the constants (2s = 7 + 1) instead of subtracting when one crosses the '=' sign; 6 skips the final division by 2; 19 is the total on a shelf, not the size of one stack.
Answer: A) 3

Key idea: Translating word problems into equations

Three steps:
1. **Pick a variable** for the unknown ('let be the number of …').
2. **Translate the words into an equation** using the operations the problem describes.
3. **Solve and answer in the original units.**

Example: 'Three times a number plus 7 equals 22. Find the number.'
Let = the number. Equation: . Solve: .
Answer: the number is 5.

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