Question

The sum of 4 consecutive integers is 70. Then the greatest among them is ________________.
A) 19
B) 23
C) 17
D) 16

Answer 1

Hint: There is no set order, as the steps used depend on what is given:
We may add, subtract, multiply, or divide an equation by a number or an expression as long as we do the same thing to both sides of the equal sign. Note that we cannot divide by zero.
Apply the distributive property as needed: $a(b + c) = ab + ac.$
Isolate the variable on one side of the equation.
When the variable is multiplied by a coefficient in the final stage, multiply both sides of the equation by the reciprocal of the coefficient.

Complete step-by-step answer:
Let the four consecutive numbers be x, x+1, x+2, x+3
The sum of four consecutive number is already given to us = 70
Therefore
\[ \Rightarrow (x) + (x + 1) + (x + 2) + (x + 3) = 70\;{\text{ }}\;\]
We need to combine x as we have four x terms in the equation. The next step is to get all of the x’s on one side of the equation and all the numbers on the other side. The same rule applies – whatever you do to one side of the equation, you must do to the other side as well!
\[
   \Rightarrow 4x + 6 = 70\; \\
   \Rightarrow 4x = 64 \\
   \Rightarrow x = 16 \\
 \]
So, the four numbers are 16, 17, 18 and 19.
Hence, the greatest number among them is 19.
Option A is the correct answer.

Note: Solving linear equations is all about isolating the variable. Depending on the equation, this may take as little as one step or many more steps. Always check if you need to simplify one or both sides of the equation first, and always check your answer.