Question

Find two consecutive even numbers such that the difference of one-half the larger and two-fifths the smaller is equal to five. . . Which equation could be used to determine the number?. 1/2(n - 2) + 2/5 n = 5. 1/2(n + 2) - 2/5 n = 5. 1/2(n + 2) + 2/5 n = 5

Answer 1

Then, it would be: 1/2 (n+2) - 2/5 n = 5

So, OPTION B is your answer.....

Answer 2

Answer: The correct option is (B)
`(1)/(2)(n+2)-(2)/(5)n=5.`

Step-by-step explanation: We are given to select the correct equation to determine two consecutive even numbers such that the difference of one-half the larger and two-fifths the smaller is equal to five.

Let, 'n' and '(n + 2)' be the two consecutive even numbers.

Then, according to the given information, the equation can be written as

`(1)/(2)* (n+2)-(2)/(5)* n=5\\\\\\\Rightarrow (1)/(2)(n+2)-(2)/(5)n=5\\\\\\\Rightarrow (5(n+2)-4n)/(10)=5\\\\\Rightarrow 5n+10-4n=50\\\\\Rightarrow n=50-10\\\\\Rightarrow n=40.`

So, n = 40 and n + 2 = 40 + 2 = 42.

Thus, the two even numbers are 40 and 42.

And, the required equation is
`(1)/(2)(n+2)-(2)/(5)n=5.`

Option (B) is correct.