Question

instructions
choose the best answer. if necessary, use the paper you were given.
question
the average (arithmetic mean) of three numbers is equal to 50. if one of the numbers is 10, what is the sum of the other two numbers?
o 40
o 90
o 140
o 150

Explanation:

Step1: Use the average formula

The formula for the arithmetic mean (average) of \(n\) numbers \(x_1,x_2,\cdots,x_n\) is \(\bar{x}=\frac{x_1 + x_2+\cdots+x_n}{n}\). Here, \(n = 3\) and \(\bar{x}=50\). So, the sum of the three numbers \(S=x_1 + x_2+x_3\) is given by \(S=n\times\bar{x}\). Substituting \(n = 3\) and \(\bar{x}=50\), we get \(S=3\times50=150\).

Step2: Find the sum of the other two numbers

Let the three numbers be \(a\), \(b\), and \(c\). We know that \(a + b + c=150\) and one of the numbers, say \(a = 10\). Then \(b + c=150 - a\). Substituting \(a = 10\) into the equation, we have \(b + c=150-10=140\).

Answer:

140 (corresponding to the third option)