A positive integer is 3 more than a multiple of 4 and 4 more than a multiple of 5. What is the least integer it could be?
I need to find the smallest positive integer that satisfies both conditions: it is 3 more than a multiple of 4 and 4 more than a multiple of 5. I can use the fact that any multiple of 4 is even, so the integer must be odd. I can also use the fact that any multiple of 5 ends with 0 or 5, so the integer must end with 9. The smallest odd integer that ends with 9 is 9 itself, but that does not work, because 9 is not 3 more than a multiple of 4. The next odd integer that ends with 9 is 19, and that works, because 19 is 3 more than 16, which is a multiple of 4, and 19 is 4 more than 15, which is a multiple of 5. Therefore, the least integer that satisfies both conditions is 19. 