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Nimfa-mama [501]
3 years ago
11

Choose the equation that could be used to find three consecutive integers whose sum is 75. n + (n + 1) + (n + 2) = 75 n + (n + 2

) + (n + 4) = 75 n + (n + 1) + (n + 3) = 75 n + (n - 1) + (n - 3) = 75
Mathematics
1 answer:
Vesna [10]3 years ago
8 0
Correct Answer:
First Option

Let the first integer be n.
Since the integers are consecutive, the integer next to n will be n+1
and so the third integer will be n+2

Therefore, the three integers are:
n , n +1, n+2

Their sum is 75. So we can write the equation as:

n + (n+1) + (n+2) = 75

This equation can be used to find n. After finding n, we can find the next two integers by finding (n+1) and (n+2)

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--

Edit: long division

We may also solve this problem using long division (see the second image). The first step is to look at the leading coefficients: since x \times x^2 is equal to x^3, the first term in the quotient will be x^2. Since x^2 \times (x+2) is equal to x^3+2x^2, we must now subtract that from x^3-4x^2-8x+8.

We repeat the same process, as shown in the image. Since we eventually get to zero, the remainder is zero, and the polynomial at the top (x^2-6x+4) is the quotient.

<em>I know this might be difficult to follow, so please comment if you have any questions.</em>

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