90cm = 0.9m

Notice that 4 x 0.9m = 3.6m
And 3 x 1.2m = 3.6m

So this means that 4 short parts is the same as 3 longer parts.

Number of big balloons on 4 short parts
= 2 x 4 = 8

Number of small balloons on 3 longer parts
= 5 x 3 = 15

Difference in balloon number
= 15 - 8 = 7

When we compare 3.6m worth of each type of part, there are 7 more small balloons than big balloons.

We can pair every 3.6m of each type into a set.

So for there to be 105 more small than big balloons,

105 ÷ 7 = 15

There has to be 15 sets.

Now in each set, there were 15 small balloons for the shorter type and 8 big balloons for the longer type. That's a total of 23 balloons


Total number of balloons in 15 sets
= 15 x 23 = 345


The idea for this question is to find a common length for both parts first, then find how many sets of this common length make up the total.

Thank you! :)

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