Question

The product of two consecutive even integers is 224. Find the integers:

A. 14 and 16
B. 12 and 18
C. 16 and 18
D. 10 and 22

Answer 1

To find the consecutive even integers whose product is 224, set up the equation x(x+2) = 224, solve the quadratic equation to get x=14 or x=-16, discard the negative value, and add 2 to 14 to find the next integer, leading to the integers 14 and 16.

Step-by-step explanation:

The question involves finding two consecutive even integers whose product is 224. To solve this, we can express the consecutive even integers as x (the smaller even integer) and x+2 (the next even integer). The equation formed is x(x+2) = 224. Solving it:

• Step 1: Expand the equation to get x^2 + 2x = 224.
• Step 2: Rearrange the equation to a standard quadratic form: x^2 + 2x - 224 = 0.
• Step 3: Factor the quadratic equation to find the integer solutions. The factors of 224 that differ by 2 are 14 and 16.
• Step 4: So the equation factors as (x - 14)(x + 16) = 0. This gives us two possible values for x: 14 or -16.
• Step 5: Neglect the negative value as we are looking for positive integers, so x = 14 is the smaller integer.
• Step 6: The next consecutive even integer will be 14+2 = 16.

Therefore, the two consecutive even integers whose product is 224 are 14 and 16, which corresponds to option A.