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The sum of two consecutive multiples of 7 is 105. What is the larger multiple?

Class 7Simple EquationsSimple Equations
  • A49
  • B52.5
  • C63
  • D56

Step-by-Step Solution

Consecutive multiples of 7 differ by 7, so take them as and . Then → → , and the multiples are 49 and 56, with 49 + 56 = 105 ✓. The larger is 56; 49 is the smaller one. Answer 52.5 halves 105 as though the two numbers were equal, and 63 is one multiple too far.
Answer: D) 56

Key idea: The balance principle

An equation is like a balance scale: LHS on one pan, RHS on the other, and the scale is level. Whatever you do to one side, you must do to the other to keep it balanced. So if you add 5 to LHS, add 5 to RHS. If you divide LHS by 3, divide RHS by 3.

Goal: isolate the variable on one side. Get by itself by undoing every operation around it, in reverse order, applied to BOTH sides.

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