The average (arithmetic mean) and median of the five numbers a,a,b,c, and c are 20 and 30, respectively. If a < b < c, what is the value of a + c?
5 numbers: a, a, b, c, c
mean = 20
--> (2a + b + 2c)/5 = 20
2a + b + 2c = 100
median = 30
---> b = 30
so we have
2a + 30 + 2c = 100
2a + 2c = 70
a+c=35
To solve this problem, we need to use the given information about the average and median of the numbers. Let's break down the steps to find the value of a + c:
Step 1: Find the sum of the five numbers.
Since the average of the numbers is 20, we can multiply the average by the total number of values to find the sum of the numbers:
Sum = Average * Number of Values = 20 * 5 = 100
Step 2: Find the value of b.
Since the median is 30, and the numbers are listed in ascending order, the value of b must be 30.
Step 3: Find the value of a + c.
We already know the sum of the five numbers is 100, and we know b is 30. So, to find the value of a + c, we subtract b (30) from the total sum (100):
a + c = 100 - 30 = 70
Therefore, the value of a + c is 70.