Problem:
The average of five consecutive odd numbers 59. What are the five numbers
Solution:
because its consecutive odd integers, add each increase by 2
let the 1st number = x
2nd number = x + 2
3rd number = x + 2 + 2 = x + 4
4th number = x + 2 + 2 + 2 = x + 6
5th number = x + 2 + 2 + 2 + 2 = x + 8
[tex]\[\begin{array}{l}average = \frac{{(x) + (x + 2) + (x + 4) + (x + 6) + (x + 8)}}{5}\\\\59 = \frac{{5x + 20}}{5}\\\\295 = 5x + 20\\\\5x = 295 - 20\\\\5x = 275\\\\x = 55\end{array}\][/tex]
1st number = 55
2nd number = 55 + 2 = 57
3rd number = 55 + 4 = 59
4th number = 55 + 6 = 61
5th number = 55 + 8 = 63
Checking:
[tex]\[\begin{array}{l}59 = \frac{{(55) + (55 + 2) + (55 + 4) + (55 + 6) + (55 + 8)}}{5}\\\\59 = \frac{{55 + 57 + 59 + 61 + 63}}{5}\\\\59 = \frac{{295}}{5}\\\\59 = 59;ok\end{array}\][/tex]
Answer:
The five numbers are 55, 57, 59, 61 and 63
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