SOLUTION: 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

Question 483541: 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
Found 2 solutions by Maths68, MathTherapy:
Answer by Maths68(1474) (Show Source): You can put this solution on YOUR website!
Let x and y are two umbers
One number is 3 less than a second number
or
x is 3 less than y
x=3-y��..(1)
Twice the second number is 3 less than 3 times the first.
Or
2y is 3 less than 3x
2y=3-3x��(2)
Put the value of x in (2)
2y=3-3(3-y)
2y=3-9+3y
2y=-6+3y
6=3y-2y
6=y
y=6
Put the value of y in (1)
x=3-y
x=3-6
x=-3
x,y = -3, 6
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!

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 = =

Substituting 9 for S in eq (i) gives us:
9 - L = - 3
- L = - 12
L, or larger number = =

-----------
Check
-----------
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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