Question 908184
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