Aballoon pump and 3 packs of balloons cost £9 altogether. a balloon pump and 4 packs of balloons cost £11 altogether. how much dose a balloon pump anf 8 packs of balloons cost?

Let the balloon pump be m and one pack of balloons be n.
we will use the given data to calculate the the price of balloon pump (m) as well as the price of one pack of balloons (n). Then, we will use these prices to calculate the requirement.

First, we know that 1 balloon pump (m) added to 3 packs of balloons (3n) costs 9£
this means that: m + 3n = 9
therefore: m = 9 - 3n > equation 1

Then, we know that one pump (m) and 4 packs (4n) cost 11£.
this means that: m + 4n = 11 > equation 2

Substitute with equation 1 in 2:
9 - 3n + 4n = 11
n = 11 - 9
n = 2£
Substitute with the value of n in equation 1:
m = 9 - 3n = 9 - 3(2) = 9 - 6 = 3£

we know to know the price of one pump and eight packs:
price = m + 8n = 3 + 8(2) = 3 + 16 = 19£

So the first thing we do is to multiply the top equation by 3. the reason i want to do this is i notice there will be a 6y on both equations and can possibly add/subtract them. so we get 6y = -3x + 27. adding that and the second equation we get 6x = 27-15 which is 12. divide by 6 and we get 2. ∴ x = 2. substituting 2 into the first equation we get 2y = -2 + 9 which is 7. divide by 2 and we get 7/2. ∴ y = 7/2, x = 2.