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iren [92.7K]
3 years ago
7

if the first and third of three consecutive odd integers are added, the result is 75 less than five times the second integers. f

ind the third integer. please show work
Mathematics
1 answer:
Anastaziya [24]3 years ago
6 0

Answer:

<em>The third integer is 27</em>

Step-by-step explanation:

Given

Represent the consecutive odd numbers with T_1, T_2; and\ T_3

Since they are consecutive odds, then

T_2 = 2 + T_1

T_3 = 2 + T_2

<em>From the first statement in the question, we have that</em>

T_1  + T_3 = 5 T_2 - 75

Required

Find the third integer

Recall that

Substitute T_2 = 2 + T_1 in T_3 = 2 + T_2

T_3 = 2 +  2 + T_1

T_3 = 4 + T_1

Substitute T_3 = 4 + T_1 and T_2 = 2 + T_1 in T_1  + T_3 = 5 T_2 - 75

T_1  + 4 + T_1 = 5(2 + T_1) - 75

Open Brackets

T_1  + 4 + T_1 = 10 + 5T_1 - 75

Collect like terms

T_1 + T_1 + 4  = 5T_1 - 75 + 10

2T_1 + 4  = 5T_1 - 65

Collect like terms

2T_1  -  5T_1  = - 65 - 4

-3T_1   = - 69

Divide both sides by -3

\frac{-3T_1}{-3}   = \frac{- 69}{-3}

T_1 = 23

Recall that T_3 = 4 + T_1

T_3 = 4 + 23

T_3 = 27

<em>The third integer is 27</em>

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