Find three consecutive numbers whose sum is 420.
The first thing we need to know is that we’re dealing with three consecutive numbers. If our first number is 𝑎, our second number is one more than that, 𝑎 plus one. If our first number was nine, our second number would be 10, 𝑎 plus one. And that means that our third value would be two more than our first value, 𝑎 plus two.
If our first value was nine, our third value would be 11. We can use 𝑎, 𝑎 plus one, and 𝑎 plus two to represent our three consecutive numbers. The sum of these numbers, adding them all together, would look like this: 𝑎 plus 𝑎 plus one plus 𝑎 plus two is equal to 420.
To solve this equation, we combine our like terms. 𝑎 plus 𝑎 plus 𝑎 equals three 𝑎. One plus two equals three. So 𝑎 plus three is equal to 420. We want to solve for 𝑎. So we subtract three from both sides. On the left, we’re left with three 𝑎 is equal to 417. We can divide by three on the left and the right. Three divided by three cancels out. 𝑎 is equal to 417 divided by three which is 139. Our 𝑎-value, our first value, is 139, which makes the next two consecutive numbers 140 and 141.
To confirm that we’ve solved this correctly, we can add 139, 140, and 141. When you add those three values together, you get 420. That is a confirmation of our three consecutive numbers whose sum is 420: 139, 140, 141.