Answer:
The third integer is 27
Step-by-step explanation:
Given
Represent the consecutive odd numbers with [tex]T_1, T_2; and\ T_3[/tex]
Since they are consecutive odds, then
[tex]T_2 = 2 + T_1[/tex]
[tex]T_3 = 2 + T_2[/tex]
From the first statement in the question, we have that
[tex]T_1 + T_3 = 5 T_2 - 75[/tex]
Required
Find the third integer
Recall that
Substitute [tex]T_2 = 2 + T_1[/tex] in [tex]T_3 = 2 + T_2[/tex]
[tex]T_3 = 2 + 2 + T_1[/tex]
[tex]T_3 = 4 + T_1[/tex]
Substitute [tex]T_3 = 4 + T_1[/tex] and [tex]T_2 = 2 + T_1[/tex] in [tex]T_1 + T_3 = 5 T_2 - 75[/tex]
[tex]T_1 + 4 + T_1 = 5(2 + T_1) - 75[/tex]
Open Brackets
[tex]T_1 + 4 + T_1 = 10 + 5T_1 - 75[/tex]
Collect like terms
[tex]T_1 + T_1 + 4 = 5T_1 - 75 + 10[/tex]
[tex]2T_1 + 4 = 5T_1 - 65[/tex]
Collect like terms
[tex]2T_1 - 5T_1 = - 65 - 4[/tex]
[tex]-3T_1 = - 69[/tex]
Divide both sides by -3
[tex]\frac{-3T_1}{-3} = \frac{- 69}{-3}[/tex]
[tex]T_1 = 23[/tex]
Recall that [tex]T_3 = 4 + T_1[/tex]
[tex]T_3 = 4 + 23[/tex]
[tex]T_3 = 27[/tex]
The third integer is 27
