Find three consecutive intergers

Question

such that two times the first interger, plus three times the second, minus the third, is equal to twent-one. Then 

write an equation using the unknows

solve the equations to find the intergers

Answer 1

Hey Leah

 

 

Consecutive integers are integers that follwo in order. For example: 1 2 3 and so on.  if you notice they are increase by one to previous one. so let assume that n ,n+1 and (n+1)+1=n+2  are consecutive integers.

 

Given that 2 times the first integer i.e 2*n  + three times second integer i.e 3(n+1) - third integer (n+2) = 21

 

if you write above in equation    2n + 3(n+1)-(n+2) =21

                                               2n+3n+3 -n-2 = 21

                                               5n+3-n-2=21 --> 4n+1 = 21 --> 4n = 21-1 --> 4n = 20 --> n = 20/4=5

 

 

so the consecutive integers are   n, n+1 and n+2   5,6,7

 

 

Hope this helps

 

-Naidu

 

     

 

Answer 2

I = first integer

I + 1 = second integer

I + 2 = third integer

 

2(I) + 3(I + 1) - (I + 2) = 21

2I + 3I + 3 - I - 2 = 21

4I + 1 = 21

4I = 20

I = 5

 

The integers are 5, 6, and 7.