Question 252900
When n is divided by 5, the remainder is 4. When n is divided by 4, the remainder is 3.  If  0 <  n  < 100, what is one possible value of n ? 


n/5 = x + 4/5
n/4 = y + 3/4


multiply first equation by 5 to get:


n = 5x + 4


multiply second equation by 4 to get:


n = 4y + 3


your 2 equations become:


n = 5x + 4
n = 4y + 3


since both expressions equal to n, then they are equal to each other so you get:


5x + 4 = 4y + 3


solve for x to get:


x = (4y-1)/5


if y = 1, then x = 3/5.


the assumption is that you want a whole number (integer) so this answer is not good.


if the numerator was 15, then you would get 15/5 = 3.


set your numerator equal to 15 and solve for y to get:


4y - 1 = 15
add 1 to both sides to get 4y = 16
divide both sides by 4 to get y = 4


if y = 4, then x = 15/5 = 3 which should satisfy the equation.


you get x = 3 and y = 4.


your two original equations were:


n/5 = x + 4/5
n/4 = y + 3/4


substitute 3 for x and 4 for y to get:


n/5 = 3 + 4/5
n/4 = 4 + 3/4


multiply first equation by 5 and second equation by 4 to get:


n = 5*3 + 4
n = 4*4 + 3


solve for n to get:


n = 19
n = 19


one of your possible values for n = 19.


19/5 = 3 with a remainder of 4.
19/4 = 4 with a remainder of 3.