Question

Five times the sum of three consecutive even integers is the same as 290 more than 5 times the largest integer. Find the integers.

A) -10, -8, -6
B) 6, 8, 10
C) -12, -10, -8
D) 8, 10, 12

Answer 1

After setting up the equation based on the consecutive even integers and simplifying, we solve to find that the smallest integer is 28. However, this result does not match the options given in the question, suggesting there might be an error in the problem statement or answer choices.

Step-by-step explanation:

To solve this problem, let's designate the three consecutive even integers as x, x + 2, and x + 4. By the problem's statement, we know that:

5(x + (x + 2) + (x + 4)) = 5(x + 4) + 290

Simplifying this equation:

5(3x + 6) = 5x + 20 + 290

15x + 30 = 5x + 310

Combining like terms gives:

15x - 5x = 310 - 30

10x = 280

Dividing by 10:

x = 28

The smallest integer in the sequence is 28, so the others are 30 and 32.

However, this set is not among the answer choices provided. Let's ensure we did not make a calculation mistake:

5(3x + 6) = 15x + 30

5(x + 4) + 290 = 5x + 20 + 290 = 5x + 310

Subtracting 5x on both sides and subtracting 30 on both sides:

15x + 30 - 5x = 310 - 30

10x = 280

x = 28 (as calculated earlier). Since this is not in the options and the equation has been checked for accuracy, there may be a mistake in the problem statement or the provided options.