Question

Four times the sum of three consecutive integers is 156

Answer 1

The question asks to find three consecutive integers whose sum, multiplied by four, equals 156. By representing the first integer as x, and forming an equation based on the given information, we solve to find that the consecutive integers are 12, 13, and 14, which satisfy the equation when verified.

Step-by-step explanation:

The student's question involves solving for three consecutive integers whose sum, when multiplied by four, equals 156. To begin, let's represent the first integer as x. Accordingly, the next two consecutive integers can be represented as x+1 and x+2. The equation based on the problem is then 4(x + x+1 + x+2) = 156.

Simplifying the equation:

• 4(3x + 3) = 156
• 12x + 12 = 156
• 12x = 156 - 12
• 12x = 144
• x = 144 / 12
• x = 12

Therefore, the first integer is 12, the second integer is 13, and the third integer is 14.

To verify:

• (12 + 13 + 14) * 4 = 156
• 39 * 4 = 156
• 156 = 156

The solution matches the given problem, confirming that the integers 12, 13, and 14 are the correct answers.

Answer 2

51, 52 and 53

Step-by-step explanation:

Let the numbers be x, x+1 and x+2

x+x+1+x+2=156

3x+3=156

subtract 3 from both sides

3x=156-3

3x=153

divide both sides by 3

x=156/3

x=51

x+1=52

x+2=53

Hence, the integers are 51, 52 and 53.