Video: Solving One-Variable Equations

Find three consecutive numbers whose sum is 420.

02:25

Video Transcript

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 π‘Ž, our second number is one more than that, π‘Ž plus one. If our first number was nine, our second number would be 10, π‘Ž plus one. And that means that our third value would be two more than our first value, π‘Ž plus two.

If our first value was nine, our third value would be 11. We can use π‘Ž, π‘Ž plus one, and π‘Ž plus two to represent our three consecutive numbers. The sum of these numbers, adding them all together, would look like this: π‘Ž plus π‘Ž plus one plus π‘Ž plus two is equal to 420.

To solve this equation, we combine our like terms. π‘Ž plus π‘Ž plus π‘Ž equals three π‘Ž. One plus two equals three. So π‘Ž plus three is equal to 420. We want to solve for π‘Ž. So we subtract three from both sides. On the left, we’re left with three π‘Ž is equal to 417. We can divide by three on the left and the right. Three divided by three cancels out. π‘Ž is equal to 417 divided by three which is 139. Our π‘Ž-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 131 [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.

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