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# Help!

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Tomorrow is my exam and I came across this question in my practice paper. I hate this type of questions a lot. Can you help? The question is:
The sum of three numbers is 7656. The first number is 1099 more than the second number. The third number is 877 less than the second number. Find the value of the second number.

May 11, 2017

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The sum of three numbers is 7656.

The first number is 1099 more than the second number.

The third number is 877 less than the second number.

Find the value of the second number.

Let n1 = Number 1

Let n2 = Number 2

Let n3 = Number 3

$$\small{ \begin{array}{|rcll|} \hline n_1+n_2+n_3 &=& 7656 \quad n_1 = 1099 +n_2 \quad n_3 = n_2-877 \\ (1099 +n_2)+n_2+(n_2-877) &=& 7656 \\ 1099 +n_2+n_2 +n_2-877 &=& 7656 \\ 1099 +3n_2-877 &=& 7656 \\ 3n_2+ 1099 -877 &=& 7656 \\ 3n_2+ 222 &=& 7656 \quad & | \quad -222 \\ 3n_2 &=& 7656 - 222 \\ 3n_2 &=& 7434 \quad & | \quad :3 \\ n_2 &=& \frac{7434}{3} \\ \mathbf{n_2} & \mathbf{=} & \mathbf{2478} \\\\ n_1 &=& 1099 +n_2 \quad & | \quad n_2 = 2478 \\ n_1 &=& 1099 +2478 \\ \mathbf{n_1} & \mathbf{=} & \mathbf{3577} \\\\ n_3 &=& -877 +n_2 \quad & | \quad n_2 = 2478 \\ n_3 &=& -877 +2478 \\ \mathbf{n_3} & \mathbf{=} & \mathbf{1601} \\ \hline \end{array} }$$

The second number is 2478

May 11, 2017
edited by heureka  May 11, 2017
edited by heureka  May 11, 2017
edited by heureka  May 11, 2017