The first of three numbers is 8 less than the second number and 3 more than twice the third number. Their sum is 89. Find the numbers.

Question

Help me please! Need answer quickly 

Answer 1

Let F = the first number;  S = second number;  T = third number
 
First, translate the phrases into precise, concise math expressions (with variables and operations);
  "the first of three numbers is 8 less than the second number..."     means   F = S - 8      eq1
  "... and 3 more than twice the third number."         means   F = 2*T + 3           eq2
  "Their sum is 89"     means    F + S + T = 89           eq3
  "Find the numbers."      means      report F, S, T
 
Now, the math:
   To get rid of F and S (and put everything in terms of T),  put eq1 and eq2 into eq3:
                             F        +             S            +  T = 89
                             F        +    (   F    + 8 )     + T  = 89
                     ( 2*T + 3 ) +  ( (2*T + 3) + 8 ) + T = 89
                            5*T + 14 = 89                (collect T's and constants)
                                 5*T = 75                  (subtract 14 from both sides)
                                     T = 15                 (divide both sides by 5)
 
Then, put T=15 into eq2,     F = 2*15 + 3
                                            F = 33
 
O.K., not put 15 and 33 into eq3:           33 + S + 15 = 89
                                                              S = 41         
 
Checking:
      Is  33 = 41 - 8  ?    yes.
      Is  33 = 2*15 + 3   ?      yes.
      Is 33 + 41 + 15 = 89  ?     yes.

Answer 2

let x=the first number

x+8=the second number (the second is 8 more than the first)

(1/2)(x-3)=the third number (to go from the first to the third you have to subtract 3 from the first and then take half of what's left-it says "the first is 3 more than twice the third")

add them together to get 89

x+(x+8)+(1/2)(x-3)=89

x+x+8+(1/2)x-(1 1/2)=89

(2 1/2)x+8-(1 1/2)=89

(2 1/2)x+6 1/2=89

2.5x+6.5=89

2.5x=89-6.5

2.5x=82.5

25x=825

x=825/25

x=33

x+8=41

(1/2)(x-3)=(1/2)(33-3)=(1/2)(30)=15

33+41+15=89

33 is 8 less than 41

33 is 3 more than two times 15