The sum of two consecutive odd integers is 284. Write an equation and solve to find the two integers.

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Equation:
Let the first odd integer be \( x \). Then the next consecutive odd integer is \( x + 2 \).

\[ x + (x + 2) = 284 \]

Solve for \( x \):
\[ 2x + 2 = 284 \]
\[ 2x = 282 \]
\[ x = 141 \]

So, the two consecutive odd integers are \( 141 \) and \( 143 \).

We need to understand how to set up the equation to solve this. If they are consecutive odd integers, that means they're two odd numbers that are next to each other, like 3 and 5 or 27 and 29. There's always a two-integer difference between the two numbers since they're both odd, so we'll use that to set up our equation. Let's make the smaller integer x. That will make the larger integer x+2, since there is a difference between them of 2. That means our equation is x+x+2=284 or 2x+2=284. When we subtract 2 from each side and then divide by two, we'll get x=141, the first integer. That means the two integers are 141 and 143.

Answered by Sphinx | 2024-06-10

The two consecutive odd integers that sum to 284 are 141 and 143. We define the first integer as x and the second as x + 2 , leading to the equation 2 x + 2 = 284 . Solving the equation gives us x = 141 and the next integer as 143.
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Answered by Sphinx | 2024-09-03