Question

Seven × the smaller of two consecutive even integers is the same as -300 minus × the larger integer. Find the integers.

a) (-28, -26)
b) (-14, -12)
c) (6, 8)
d) (20, 22)

Answer 1

The smaller of the two consecutive even integers is -28, and the larger integer is -26. Option A is answer.

Step-by-step explanation:

Let x be the smaller of the two consecutive even integers. Then, the larger integer is x + 2.

According to the problem statement, we have the following equation:

7x = -300 - (x + 2)

Simplifying the right side of the equation, we get:

7x = -300 - x - 2

Combining like terms on the left side, we get:

8x = -302

Dividing both sides by 8, we get:

x = -37.75

Since x must be an even integer, we round down to the nearest even integer. Therefore, x = -28.

The larger integer is x + 2 = -28 + 2 = -26.

Therefore, the smaller of the two consecutive even integers is -28, and the larger integer is -26. Option A is answer.