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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

User Digiwand
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2 Answers

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

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

User Kerwan
by
8.5k points
3 votes

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.

User Maxluzuriaga
by
8.0k points

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