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Deepa thinks of a number, multiplies it by 6, subtracts 9 from the product and gets 45. Which pair of steps works backwards to her number?

Class 7Simple EquationsSimple Equations
  • ADivide by 6, then add 9
  • BAdd 9, then divide by 6
  • CSubtract 9, then divide by 6
  • DAdd 9, then multiply by 6

Step-by-Step Solution

Undo the operations in REVERSE order, each by its inverse. The last thing Deepa did was subtract 9, so add 9 first: 45 + 9 = 54. The first thing she did was multiply by 6, so divide last: 54 ÷ 6 = 9. Her number is 9, and 6(9) − 9 = 45 ✓. Dividing first gives 45 ÷ 6 = 7.5 and never recovers her number — undoing in the wrong order is the trap.
Answer: B) Add 9, then divide by 6

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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