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.

CalculatorPlease9987
May 11, 2017

#1**0 **

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 n_{1} = Number 1

Let n_{2} = Number 2

Let n_{3} = 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**

heureka
May 11, 2017