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Question 908184: The difference between the sum of four cinsecutive odd numbers and three consecutive even numbers is 20.Also,the largest even number is 5 more than the largest odd number.what is the sum of the smallest odd number and the smallest even number?
option
1.75
2.77
3.85
4.cannot be determined
5.none of these
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! let a = the 1st odd number
let b = the 1st even number
:
"The difference between the sum of four consecutive odd numbers and three consecutive even numbers is 20."
(a+(a+2)+(a+4)+(a+6)) - (b+(b+2)+(b+4)) = 20
Combine like terms
(4a+12) - (3b+6) = 20
remove bracket, minus changes the signs in the brackets
4a + 12 - 3b - 6 = 20
4a - 3b + 6 = 20
4a - 3b = 20 - 6
4a - 3b = 14
:
"Also, the largest even number is 5 more than the largest odd number.
(b+4) = (a+6) + 5
b + 4 = a + 11
b = a + 11 - 4
b = a + 7
:
In the 1st simplified equation replace b with (a+7)
4a - 3(a+7) = 14
4a - 3a - 21 = 14
a = 14 + 21
a = 35 is the 1st odd number
and
b = 35 + 7
b = 42 is the 1st even number
:
"what is the sum of the smallest odd number and the smallest even number?
35 + 42 = 77
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