Mathematical Problem

x+y=m+2 4x+5y=6m+3

4x+5y=6m+3
4x+4y+y = 6m+3
4(x+y)+y = 6m+3
4(m+2)+y = 6m+3
4m+8+y = 6m+3
y = 2m-5
m = (y+5)/2

Here, m = 3 is smallest when y = 1, so m>=3

x+y=m+2
y = m+2-x

From above, 4(m+2)+y = 6m+3
4(m+2)+m+2-x = 6m+3
x = 7-m
m = 7-x

Here, m = 6 is largest when x = 1, so m<=6

Combine the two ranges, 3=<=6.

2007-06-14 12:11:44 補充：
3 =

2007-06-14 12:12:46 補充：
Don't why can't show ar,Anyway, the answer is "3 less than or equal to m less than or equal to 6".

2007-06-14 14:10:24 補充：
Thanks T#, I thought x and y are positive integers.So T#'s answer is closer, but I am just not sure that whether 0 is positive.I guess it's neither positive nor negative.If x and y can't equal 0, then final answer will be: 2.5 < m < 7

First, since
m = x + y - 2 and m = (4x + 5y - 3)/6,

we can combine the two equations as follows:
x + y - 2 = (4x + 5y - 3)/6

i.e.
2x + y = 9 ......... (*)

Now, plot the graph of the equation (*) and you will see that the possible range of x which satisfies the condition x, y are both positive is 0 < x < 4.5.

Also, note that (*) can be rewritten as follows:
x + y - 2 = 7 - x

and so to find the range of m is equivalent to find the range of 7 - x where 0 < x < 4.5. Thus, we can conclude that the range of m is 2.5 < m < 7.

我想補充一下回答者(lovelyfatsimon)
x and y should be positive number. it means x and y can be "0" (zero).
ie:. 0.1, 0.15.....etc...^^
so,
x+y=m+2 4x+5y=6m+3

4x+5y=6m+3
4x+4y+y = 6m+3
4(x+y)+y = 6m+3
4(m+2)+y = 6m+3
4m+8+y = 6m+3
y = 2m-5
m = (y+5)/2

Here, m = 3 is smallest when y = 1, so m>=3 ----- incorrect^^
(here, m =2.5 is smallest when y = 0 , so m>=2.5) ----- correct ^^

x+y=m+2
y = m+2-x

From above, 4(m+2)+y = 6m+3
4(m+2)+m+2-x = 6m+3
x = 7-m
m = 7-x

Here, m = 6 is largest when x = 1, so m<=6 ----- incorrect^^
(here, m =7 is smallest when x = 0 , so m<=7) ----- correct ^^

Combine the two ranges, 2.5<= x <=7.

x+y=m+2
4x+5y=6m+3
4x+5y=6m+3 = 4(m+2) + y = 6m+3
4m + 8 + y = 6m +3
2m = 5+y
m = (5 + y) /2
because x,y are positive numbers
so, numeral range of m is 2.5 =< m < +infinity

2007-06-16 00:46:24 補充：
應該2.5