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.