Four consecutive whole numbers add up to 74. Find the smallest of the four.

Class 8Linear Equations in One VariableLinear Equations

A17
B18
C18.5
D20

Step-by-Step Solution

Take them as

x, x + 1, x + 2, x + 3

. Then

4 x + 6 = 74

→

4 x = 68

→

x = 17

, and 17 + 18 + 19 + 20 = 74. Simply dividing 74 by 4 gives the trap 18.5, which ignores the +6 contributed by the three step-ups; 20 is the largest of the four, not the smallest.

Answer: A) 17

Key idea: Equations with fractions

Multiplying both sides by the LCM of denominators turns fractions into whole numbers in one move.

Example:

\frac{x}{2} + \frac{1}{3} = \frac{5}{6}

. LCM of 2, 3, 6 = 6. Multiply every term by 6:

6 \times \frac{x}{2} + 6 \times \frac{1}{3} = 6 \times \frac{5}{6} 3 x + 2 = 53 x = 3, x = 1

.

Verify:

\frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6}

. ✓

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