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
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 = =
