A positive number is 30 less than its square. Find the number.

First, let us label the unknown, the positive number we are asked to solve. For example, we can use "n". Hence n^2 is its square. What does it mean to be 30 less? Another way to phrase is that it means that the square, n^2, exceeds n by 30. So if we add 30 to n we get n^2. In equation form this can be written as

n+30 = n^2

n^2 - n - 30 = 0

Here you should get two solutions. Since the problem says 'positive number', this will limit your solution.

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For the other two, I'll give you something to start with and you can write the equations on your own.

2) Consecutive can colloquially mean "the term in the sequence that follows". So if we choose n again as our integer, n+1 is its consecutive number. Products between two numbers can be written as xy, where x and y are two numbers.

3) Trickier in terms of wording, but same concepts apply as above.

What does it mean to have a sum of squares? ex. x^2 + y^2

What does it mean to have two consecutive positive even integers? ex. 2 and 4 and 2n and 2(n+1) [can you justify the last example?]

If you want me to verify if you set up the equations correctly, you may ask.