+864 How many of the 1000 smallest positive integers are congruent to 7 modulo 29?
+1790 We can write a handy equation to solve this problem.
First, let's set a variable. Let's set x as a positive integer.
Any number congruent to 7 modulo 29 can be written in the form
\(29x+7\) since it is 7 greater than a factor of 29.
thus, we can write the inequality
\(29x+7\leq 1000\)
Setting the two to equal and solving for x, we have
\(29x+7=1000\\ 29x=993\\ x \approx 34.24\)
Rounding down, we find x is 34.
So our answer is 34.
Thanks! :)
the answer is \(34\)
