Find three consecutive even numbers whose sum is 2832.
Three consecutive even numbers are any three even numbers that follow each other on a number line, for example, 20, 22, and 24. We would calculate the sum of these by adding the three numbers. This would give us an answer of 66. This is clearly a long way away from 2832. We could try and solve this problem using trial and improvement. However, this method would be very time-consuming. A better way to solve the problem would be setting up an algebraic equation.
We know that any even number is a multiple of two. This means that if we let 𝑛 be any integer, then two 𝑛 will be an even number as multiplying any integer by two gives us an even number. As every even number is two more than the preceding one, three consecutive even numbers would be two 𝑛, two 𝑛 plus two, and two 𝑛 plus four. The sum of these could be written as an expression, two 𝑛 plus two 𝑛 plus two plus two 𝑛 plus four. We’re told in this case that this is equal to 2832.
In order to solve this equation, we firstly need to group or collect our like terms. Two 𝑛 plus two 𝑛 plus two 𝑛 is equal to six 𝑛, and two plus four is equal to six. The equation simplifies to six 𝑛 plus six is equal to 2832. We can then solve this equation by firstly subtracting six from both sides. This gives us six 𝑛 is equal to 2826. Finally, we divide both sides of this new equation by six. We can divide 2826 by six using the bus-stop method. This gives us an answer of 471. Our value of 𝑛 is 471. Our first even number was equal to two 𝑛. Two multiplied by 471 is 942.
The three consecutive even numbers that sum to 2832 are 942, 944, and 946. We can check this by adding the three numbers, which gives us a total of 2832.