If p is an integer and 3 is the remainder when 2p+7 is divided by 5, then what is the value of p?
Here is my steps:
(2p+7)/5 = 3
2p+7= 15
2p= 8
p=4
I don't know where I got wrong but the correct answer is 3
Thanks in advance
You're going to ask me why, but you "can't do" $\displaystyle \frac {2p + 7} 5 = 3$ for determining the remainder when 2p+7 is divided by 5.
What $\displaystyle \frac {2p + 7} 5 = 3$ means is that 3 is the result of dividing 2p+7 by 5.
What you want to say is something like this.
When you divide 2p+7 by 5, you get some integer (call it q) plus 3 left over.
Thus 2p+7 = 5q + 3.
(Or you could say: if you subtract 3 from 2p+7, then its remainder when divided by 5 will be zero, so 2p+7 - 3 is an exact multiple of 5.)
So you have 2p+4 = 5q and so p+2 = 5q / 2.
So you know that q must be an even number or 5q/2 won't be an integer.
So you also got (p+2) / 5 = q
You can also see that p+2 must be divisible by 5, or q won't be an integer either.
Turns out there are lots of answers to this problem, but the simplest one is a value of p such that p+2 is divisible by 5. So see what happens if you pick p+2 = 5.