<PRE><B>Question 483541</B>


one number is 3 less than a second number. twice the second number is 3 less than 3 times the first. find the two numbers


The second number is obviously the larger number, and will be named L
The other number will be the smaller and named S

Since the smaller number, or S is 3 less than the larger, then we can say that S = L – 3 ___ S – L = - 3


Also, since twice the second number (larger number) is 3 less than 3 times the other number (smaller number), we can say that: 2L = 3S – 3 ______ - 3S + 2L = - 3


We now have the following simultaneous equations:

     S – L = - 3 -------- eq (i)
– 3S + 2L = - 3 ----- eq (ii)
  2S – 2L = - 6 -------- eq (iii) ----- multiplying eq (i) by 2
 – S = - 9 ------ Adding eq (ii) and eq (iii) 
S, or smaller number = {{{(-9)/-1}}} = {{{highlight_green(9)}}} 


Substituting 9 for S in eq (i) gives us: 
9 - L = - 3 
- L = - 12

L, or larger number = {{{(-12)/-1}}} = {{{highlight_green(12)}}} 


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Check
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Smaller #: 9
Larger #: 12


Smaller # (9) is 3 less than larger # (12)


Twice larger # (12) = 2(12) = 24
Thrice smaller # (9) = 3(9) = 27 


Twice larger # (24) is 3 less than thrice smaller # (27)


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