Two Consecutive even numbers are such that half of the larger number exceeds one-forth of the smaller number by 5.then the larger number is ??

1)16
2)18
3)32
4)34

Plse help me this question

smaller ---- x

larger ------ x+2

(1/2)(x+2) - (1/4)x = 5

solve for x

Answer is right ☺

To solve this problem, let's assume the smaller of the two consecutive even numbers is "x".

Since they are consecutive even numbers, the larger number will be "x + 2" because it is the next even number after "x".

Given that half of the larger number exceeds one-fourth of the smaller number by 5, we can write the equation as:

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

To solve for x, we need to simplify the equation step by step:

Multiply everything by 4 to get rid of the fractions:

2(x + 2) = x + 20

Distribute 2:

2x + 4 = x + 20

Subtract x from both sides:

2x - x + 4 = 20

Simplify:

x + 4 = 20

Subtract 4 from both sides:

x = 16

So, the smaller number is 16.

The larger number is x + 2, which is 16 + 2 = 18.

Therefore, the correct answer is option 2) 18.