The second of three numbers is two-thirds as great as the third number but one more than the first. If the sum of the three numbers is 41, find the numbers.

Question

This is number word problem.  I'm getting 

2/3x + 2/3x + 1 + x =41

Answer 1

3 numbers

 

1st  2/3x-1

2nd 2/3x

third x

 

(2/3x-1) + 2/3x + x = 41

 

7/3x = 42

 

x = 18 (third number)

 

2/3x = 12 (2nd number)

 

2/3x-1 = 11 (first number)

Your setup looks like second number is one more than the first (that's good) but the second number is also 1 more than 2/3 the third, but the second is only supposed to be 2/3 the third

Answer 2

x=1st

x+1=2nd

if the second number is 2/3 as great as the third number then the third number is 3/2 as great as the second number

therefore...

(3/2)(x+1)=3rd

add

x+(x+1)+(3/2)(x+1)=41

x+x+1+(3/2)x+(3/2)=41

(3 1/2)x+ 2 1/2=41

(7/2)x+5/2=41

multiply both sides by 2

7x+5=82

7x=82-5

7x=77

x=77/7

x=11 (first)

x+1=12  (second)

(3/2)(12)=18  (third)