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Find three consecutive numbers whose sum is 420.
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The first thing we need to know is that weβre dealing with three consecutive numbers.
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If our first number is π, our second number is one more than that, π plus one.
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If our first number was nine, our second number would be 10, π plus one.
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And that means that our third value would be two more than our first value, π plus two.
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If our first value was nine, our third value would be 11.
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We can use π, π plus one, and π plus two to represent our three consecutive numbers.
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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.
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To solve this equation, we combine our like terms.
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π plus π plus π equals three π.
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One plus two equals three.
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So π plus three is equal to 420.
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We want to solve for π.
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So we subtract three from both sides.
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On the left, weβre left with three π is equal to 417.
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We can divide by three on the left and the right.
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Three divided by three cancels out.
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π is equal to 417 divided by three which is 139.
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Our π-value, our first value, is 139, which makes the next two consecutive numbers 140 and 141.
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To confirm that weβve solved this correctly, we can add 131 [139], 140, and 141.
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When you add those three values together, you get 420.
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That is a confirmation of our three consecutive numbers whose sum is 420: 139, 140, 141.