Find three consecutive odd intergers

Question

such that three times the first interger, plus four times the second, equals negative thirteen times the third intergers.

then I have too

write an equation using the intergers

solve the equation to find the intergers

Answer 1

Leah,

 

The question asks for consecutive odd integers so we nee to write these as:

 

1st = 2n + 1

2nd = 2n + 3

3rd = 2n + 5

 

No we can follow through the process and write:

 

3(2n + 1) + 4(2n + 3) = -13(2n + 5)

 

simplifying:

 

6n + 3 + 8n + 12 = -26n - 65

 

collecting terms:

 

14n + 26n = -65 - 15

 

40n = -80

 

n = -2

 

Our 3 consecutive odd integers are:

 

1st = 2n + 1 = -4 + 1 = -3

2nd = 2n + 3 = -4 +3 = -1

3rd = 2n + 5 = -4 + 5 = +1

 

Check:

 

3(-3) +4(-1) = -13(+1)

 

- 9 - 4 = -13 

Answer 2

first integer = n

second = n + 1

third = n + 2

 

3n + 4(n + 1) = -13(n + 2)

3n + 4n + 4 = -13n - 26

7n + 4 = -13n - 26

20n + 4 = -26

20n = -30

n = -3/2                Not an integer.