Here is the problem text:
"When the positive integer n is divided by 3, the remainder is 2 and when n is divided by 5 the remainder is 1. What is the least possible value of n?"
I got the answer by just subbing in values, 11 is the answer. But what I'm trying to do now is write an algebraic solution. So I tried to figure out how to represent each part of the problem with an equation and this is what I have:
n is divided by 3, the remainder is 2: (3n + 2) / 3
n is divided by 5, the remainder is 1: (5n + 1) / 5
When I subbed in some values, the equations seemed to kick out the correct remainder. But, how do I sove the two equations for n? If I set them equal to each other and try to solve for n, I don't get a solution.
1) (3n + 2) / 3 = (5n + 1) / 5
2) 15 * (3n + 2) / 3 = 15 * (5n + 1) / 5 (clear the denominator by multiplying by 15)
3) 15n + 10 = 15n + 3
4) 15n - 15n = 3 - 10
5) 0 = -7
This is where I'm stuck - obviously this doesn't return a solution. Are my equations wrong? Is trying to solve them for each other wrong?
Thanks for any assistance!
"When the positive integer n is divided by 3, the remainder is 2 and when n is divided by 5 the remainder is 1. What is the least possible value of n?"
I got the answer by just subbing in values, 11 is the answer. But what I'm trying to do now is write an algebraic solution. So I tried to figure out how to represent each part of the problem with an equation and this is what I have:
n is divided by 3, the remainder is 2: (3n + 2) / 3
n is divided by 5, the remainder is 1: (5n + 1) / 5
When I subbed in some values, the equations seemed to kick out the correct remainder. But, how do I sove the two equations for n? If I set them equal to each other and try to solve for n, I don't get a solution.
1) (3n + 2) / 3 = (5n + 1) / 5
2) 15 * (3n + 2) / 3 = 15 * (5n + 1) / 5 (clear the denominator by multiplying by 15)
3) 15n + 10 = 15n + 3
4) 15n - 15n = 3 - 10
5) 0 = -7
This is where I'm stuck - obviously this doesn't return a solution. Are my equations wrong? Is trying to solve them for each other wrong?
Thanks for any assistance!