a,b,c,d, and e are integers; M is their average; and S is their sum. What is the ratio of S to M?
Say a b c d e are 1 2 3 4 5.
1+2+3+4+5= 15
(1+2+3+4+5)/5= 3
ratio is 3:15, or 1:5
try this with any set of numbers and it will always work
No... I tried a different set and it didn't.. Are u sure?
2 + 3 + 4 + 5 + 6 = 20
(2 + 3 + 4 + 5 + 6)/5 = 4
4:20, when simplified, is 1:5
5 + 6 + 7 + 8 + 9 = 35
(5 + 6 + 7 + 8 + 9)/5 = 7
7:35 = 1:5
300 + 301 + 302 + 303 + 304 = 1510
(300 + 301 + 302 + 303 + 304)/5 = 302
302:1510 = 1:5
I promise you, the ratio will always be 1 to 5
Proof for all values:
let a+b+c+d+e = S
let M be the average
M = S/5
5M = S
then S/M = 5/1
or
S : M = 5 : 1
To find the ratio of S (the sum of the integers) to M (their average), you need to understand the relationship between S and M.
First, let's establish the formulas for S and M:
S = a + b + c + d + e (the sum of the integers)
M = (a + b + c + d + e) / 5 (the average of the integers)
To find the ratio of S to M, we divide S by M:
Ratio = S / M
Substituting the formulas for S and M into the ratio equation, we get:
Ratio = (a + b + c + d + e) / ((a + b + c + d + e) / 5)
Simplifying the expression, we can cancel out the common factor of (a + b + c + d + e):
Ratio = 5
Hence, the ratio of S to M is 5.