Question

Find three consecutive integers such that five times the sum of the first and −4 is 35 less than the sum of the second and third. Write the integers in order from least to greatest.

Answer 1

To find three consecutive integers based on the given condition, we set up an equation 5(n − 4) = (n + 1) + (n + 2) − 35, which upon solving gives n = − 4. Thus, the consecutive integers are − 4, − 3, and − 2.

Step-by-step explanation:

Let's start by defining the three consecutive integers. We can represent them as n (the first integer), n+1 (the second integer), and n+2 (the third integer).

According to the question, five times the sum of the first integer and −4 is 35 less than the sum of the second and third integers. We can create the following equation: 5(n − 4) = (n + 1) + (n + 2) − 35.

Now, let's solve for n:

5(n − 4) = (n + 1) + (n + 2) − 35

5n - 20 = 2n + 3 − 35

5n − 20 = 2n − 32

5n − 2n = − 32 + 20

3n = − 12

n = − 12 / 3

n = − 4