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

12m

step-by-step explanation:

square root means have of a number so have of 3 is 1.5 then multiply it by 8 and you get your answer!

first, we define the variables:

x: number of years after 1950

f (x): amount of vinyl sold.

then, with the variables defined, we have:

68594 vinyl records were sold in 1958 > f (8) = 68594

91299 vinyl records were sold in 1961 > f (11) = 91299

38720 vinyl records were sold in 1952 > f (2) = 38720

161743 vinyl records were sold in 1967 > f (17) = 161743

read more on -

step-by-step explanation: