Answered

and
an
90
(C) 11/13
(D) 9/11
21. Three consecutive even numbers are such that
one-third of the second number is equal to
one-fourth of the third number. Find the three
numbers.
(A) 4, 6, 8
(B) 8, 10, 12
(C) 12, 14, 16
(D) 2, 4, 6

Verified Answer :

GinnyAnswer

Let's call the three consecutive even numbers a, b, and c, where b is the second number and b = a + 2 and c = b + 2, since the difference between any two consecutive even numbers is 2.

According to the problem, one-third of the second number is equal to one-fourth of the third number. Therefore, we can write the equation:
\(\[ \frac{b}{3} = \frac{c}{4} \]\)

Now, since c is the third number and it is two more than b, we can substitute c with b + 2 in our equation:

\(\[ \frac{b}{3} = \frac{b + 2}{4} \]\)

To solve for b, we can cross-multiply to get rid of the fractions:

\(\[ 4b = 3(b + 2) \]\)
\(\[ 4b = 3b + 6 \]\)

Subtract 3b from both sides of the equation:

\(\[ 4b - 3b = 6 \]\)
\(\[ b = 6 \]\)

Now that we have the second number, we can find the first and third numbers using the relationships b = a + 2 and c = b + 2.

First number, a = b - 2 = 6 - 2 = 4.
Third number, c = b + 2 = 6 + 2 = 8.

The three consecutive even numbers are 4, 6, and 8.

Thus, the answer is (A) 4, 6, 8.

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