Question Video: Solving One-Variable Equations | Nagwa Question Video: Solving One-Variable Equations | Nagwa

# Question Video: Solving One-Variable Equations Mathematics • First Year of Preparatory School

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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 weβre dealing with three consecutive numbers. If our first number is π, our second number is one more than that, π plus one. If our first number was nine, our second number would be 10, π plus one. And that means that our third value would be two more than our first value, π plus two.

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

To solve this equation, we combine our like terms. π plus π plus π equals three π. One plus two equals three. So π plus three is equal to 420. We want to solve for π. So we subtract three from both sides. On the left, weβre left with three π is equal to 417. We can divide by three on the left and the right. Three divided by three cancels out. π is equal to 417 divided by three which is 139. Our π-value, our first value, is 139, which makes the next two consecutive numbers 140 and 141.

To confirm that weβ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.

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