Question 271152: If the larger of two numbers is divided by 6 and is subtracted from three times the smaller number, the result is 44. If the smaller number is increased by 4, the result is half the largest number. Find the numbers. This is so comples I do not know how to set it up. I know 3X-n/6=44 and the part +4 = 1/2n
Found 2 solutions by Greenfinch, Edwin McCravy:
Answer by Greenfinch(383)   (Show Source):
You can put this solution on YOUR website! Numbers N and n
Then 3n - (N/6)= 44
and (n + 4)= N/2
so (n+4)/3 = N/6
so 3n - (n + 4)/3 = 44
9n - n - 4 = 132
8n = 136
n = 17
N = 42
Answer by Edwin McCravy(20056)  (Show Source):
You can put this solution on YOUR website! If the larger of two numbers is divided by 6 and is subtracted from three times the smaller number, the result is 44. If the smaller number is increased by 4, the result is half the largest number.
The other tutor just gave you the equations and solved them. I think
your problem is not as much solving the equtions so much as getting
them from the words. I will show you how to get the equations from
the words.
In the following, observe what I have substituted the red parts
for from one sentence to the next, and you'll see how the equations
come from the words:
If the larger of two numbers is divided by 6 and is subtracted from three
times the smaller number, the result is 44. If the smaller number is increased
by 4, the result is half the largest number.
If L is divided by 6 and is subtracted from three times the smaller number,
the result is 44. If the smaller number is increased by 4, the result is half
the largest number.
If L is divided by 6 and is subtracted from three times the smaller number,
the result is 44. If the smaller number is increased by 4, the result is half
the largest number.
L/6 is subtracted from three times the smaller number, the result is 44. If
the smaller number is increased by 4, the result is half the largest number.
L/6 is subtracted from three times the smaller number, the result is 44. If
the smaller number is increased by 4, the result is half the largest number.
L/6 is subtracted from three times S, the result is 44. If the smaller number
is increased by 4, the result is half the largest number.
L/6 is subtracted from three times S, the result is 44. If the smaller number
is increased by 4, the result is half the largest number.
L/6 is subtracted from 3S, the result is 44. If the smaller number is
increased by 4, the result is half the largest number.
L/6 is subtracted from 3S, the result is 44. If the smaller number is
increased by 4, the result is half the largest number.
3S MINUS L/6, the result is 44. If the smaller number is increased by 4, the
result is half the largest number.
3S - L/6, the result is 44. If the smaller number is increased by 4, the
result is half the largest number.
3S - L/6, the result is 44. If the smaller number is increased by 4, the
result is half the largest number.
3S - L/6 = 44. If the smaller number is increased by 4, the result is half the
largest number.
3S - L/6 = 44. If the smaller number is increased by 4, the result is half the
largest number.
3S - L/6 = 44. If S is increased by 4, the result is half the largest number.
3S - L/6 = 44. If S is increased by 4, the result is half the largest number.
3S - L/6 = 44. S PLUS 4, the result is half the largest number.
3S - L/6 = 44. S + 4, the result is half the largest number.
3S - L/6 = 44. S + 4, the result is half the largest number.
3S - L/6 = 44. S + 4, the result is half L.
3S - L/6 = 44. S + 4, the result is half L.
3S - L/6 = 44. S + 4, the result is (1/2) L.
3S - L/6 = 44. S + 4, the result is (1/2) L.
3S - L/6 = 44. S + 4, the result is (1/2) L.
3S - L/6 = 44. S + 4 = (1/2) L.
So we have the system of equations:
Multiply the first equation through by 6 to clear of fractions:
Multiply the second equation through by 2 to clear of fractions:
Multiply the first equation through by 6 to clear of fractions:
Multiply the second equation through by 2 to clear of fractions:
Substitute  for L in the first equation:
Substitute 17 for S in
So the smaller number is 17 and the larger number is 42.
Edwin
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