Adam had 30 less balloons than billy had. after billy gave 5 balloons to adam, the number of adam's balloons was half of the number of billy's balloons. what was the number of balloons they have together?

Number of balloon they had together was 60 balloons

Explanation:

Assume the original number of balloons Billy had was x

We know that, initially, Adam had 30 less balloons than Billy. This means that:

original number of balloons Adam had was x-30

The scenario goes as follows:

i.  Billy gave 5 balloons to Adam

Number of balloons Billy has = x - 5

Number of balloons Adam has = (x-30) + 5 = x - 25

ii. When Billy gave Adam the 5 balloons, number of Adam's balloons became half the number of Billy's balloons. This means that:

Number of balloons Adam has = 0.5 * number of balloons Billy has

x - 25 = 0.5 * (x-5)

2(x-25) = x - 5

2x - 50 = x - 5

2x - x = -5 + 50

x = 45

This means that:

Initially, number of balloons Billy had = x = 45 balloons

Initially, number of balloons Adam had = x - 30 = 45 - 30 = 15 balloons

Number of balloons they have together = 45 + 15 = 60 balloons

Hope this helps :)