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

answer: the answer is (b) amie should have multiplied

step-by-step explanation: given a sphere and a cylinder with same radius and height.

let, 'r' be the radius of the cylinder and sphere and 'h' be the height of the cylinder. according to the question,

r = h.

now, the volume of the sphere will be

and the volume of the cylinder will be

therefore, we have

thus, ammie should have multiplied the volume of the sphere