Question

Write an equation and solve algebraically: Two consecutive integers have the property that when the smaller number is added to four times the larger number, the result is 29. Find the two consecutive integers.​ A) 4 and 5

B) 5 and 6
C) 6 and 7
D) 7 and 8
E) 8 and 9

Answer 1

To solve the problem, we assume that the smaller consecutive integer is x and the larger consecutive integer is x+1. We then set up an equation and solve for x, resulting in the smaller integer being 5 and the larger integer being 6.

Step-by-step explanation:

To solve this problem, let's assume that the smaller consecutive integer is x and the larger consecutive integer is x+1. According to the given information, when the smaller number is added to four times the larger number, the result is 29.

So, we can write the equation as:

x + 4(x+1) = 29

Simplifying the equation:

x + 4x + 4 = 29

Combining like terms:

5x + 4 = 29

Subtracting 4 from both sides:

5x = 25

Dividing both sides by 5:

x = 5

Therefore, the smaller consecutive integer is 5 and the larger consecutive integer is x+1 = 5+1 = 6.

So, the correct answer is B) 5 and 6.