If the sum of the five consecutive integers is 80, what is the value of sum of the least of these integers and the median of these integers? Can you explain it?
first number: a
second number: a + 1
third number: a + 2
fourth number: a + 3
fifth number: a + 4
a + a + 1 + a + 2 + a + 3 + a + 4 = 80
5 a + 10 = 80 Subtract 10 to both sides
5 a + 10 - 10 = 80 - 10
5 a = 70 Divide both sides by 5
a = 70 / 5 = 14
The numbers :
14, 15, 16, 17, 18
The least of these integers = 14
The median value of this set of numbers = 16
14 + 16 = 30
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To find the value of the sum of the least integer and the median, we need to determine the values of the consecutive integers.
Let's assume the least integer as "x".
The next four consecutive integers would be x + 1, x + 2, x + 3, and x + 4.
We can add these five integers together to obtain their sum:
x + (x + 1) + (x + 2) + (x + 3) + (x + 4) = 80
Simplifying this equation, we get:
5x + 10 = 80
Subtracting 10 from both sides:
5x = 70
Dividing both sides by 5:
x = 14
Now that we know the value of the least integer, we can find the median. The median of any set of consecutive integers is always the middle value.
So, in this case, the median would be x + 2, which is 14 + 2 = 16.
To find the sum of the least integer and the median, we add x and the median together:
14 + 16 = 30
Therefore, the value of the sum of the least integer and the median is 30.
To solve this problem, we need to find the five consecutive integers that add up to 80.
Let's assume that the least of these integers is represented by "x". Since the integers are consecutive, the next four integers would be x+1, x+2, x+3, and x+4.
According to the given condition, the sum of these five consecutive integers is 80. So, we can set up the equation:
x + (x+1) + (x+2) + (x+3) + (x+4) = 80
Now, let's simplify the equation by combining like terms:
5x + 10 = 80
Subtract 10 from both sides of the equation:
5x = 70
Divide both sides of the equation by 5:
x = 14
So, the least of these integers is 14.
To find the median of these integers, we need to arrange them in ascending order. The integers are 14, 15, 16, 17, and 18.
The median is the middle value in a set of numbers. Since we have an odd number of integers, the median would be the middle one, which is 16.
Now, we can calculate the sum of the least integer (14) and the median (16):
14 + 16 = 30
Therefore, the value of the sum of the least of these integers and the median of these integers is 30.