7. What is the smallest number of pebbles greater than 10 for which grouping them in heaps of 7 leaves

1 extra and grouping them in heaps of 5 leaves 3 extra? Show your working.

What's the answer

43

Step-by-step explanation:

So we want the number of pebbles p, when divided into groups of 7 has a remainder of 1 and when dividing by 5 leaves 3 extra.

So what does this mean? well, using division we want to say p - 1 is divisible by 7 and p - 3 is divisible by 5

So what you want to do is either count by 7s, add one to get a new number x then subtract 3 and see if it is divisible by 5, or go the other way and count by 5s, add 3 to get x then subtract 1 and see if it is divisible by 7.

To make it into a formula use (7x + 1) - 3 or (5x + 3) - 7. There may be a formula but I cannot recall it. I am going to use the formula with the 7 though, because it is easier to tell if a number is divisible by 5.

(7 (1) + 1) - 3 = 5 but less than 10 so no

(7 (2) + 1) - 3 = 12

(7 (3) + 1) - 3 = 19

26

33

40 Divisible by 5! so just add the 3 back to get 43 and that is the number of pebbles that fits the description. it is one more than 42 which is divisible by 7