The difference between the sum of the four consecutive odd numbers and sum of three consecutive even number is 20. the largest even number is 5 more than that of largest odd number.what is the sum of smallest even number and smallest odd number?
Answers
Given : The difference between the sum of the four consecutive odd numbers and sum of three consecutive even number is 20.
the largest even number is 5 more than that of largest odd number.
To Find : sum of smallest even number and smallest odd number
Solution:
Four consecutive odd number
a , a + 2 , a + 4 , a + 6
three consecutive even number
b , b + 2 , b + 4
largest even number is 5 more than that of largest odd number.
=> b + 4 = a + 6 + 5
=> b = a + 7 .... Eq 1
Sum of Four consecutive odd number
= a + a + 2 + a + 4 + a + 6 = 4a + 12
Sum of three consecutive even number
= b + b + 2 + b + 4 = 3b + 6
= 3(a + 7) + 6
= 3a + 27
4a + 12 - ( 3a + 27) = a - 15 = 20
a - 15 = 20
=> a = 35
a = 35
b = 35 + 7 = 42
a + b = 35 + 42 = 77
sum of smallest even number and smallest odd number = 77
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