Two circus clowns are blowing up balloons, but some of the balloons are popping before they can be sold. The first clown can blow up a balloon every 2 min, the second clown requires 3 min for each balloon, and every 5 min one balloon pops. How long will it take the clowns, working together, to have 76 balloons?

X = 120 minutes

it will take the clowns 120 minutes working together to have 76 balloons.

Step-by-step explanation:

Let X represent the time taken by both clowns to blow 76 balloons

The first clown can blow up a balloon every 2 min,

N1 = X/2

the second clown requires 3 min for each balloon,

N2 = X/3

and every 5 min one balloon pops

N3 = X/5

Total number of balloons after X minutes is

N = N1 + N2 - N3 = 76

X/2 + X/3 - X/5 = 76

LCM = 30

(15X + 10X - 6X)/30 = 76

Cross multiply;

19X = 76×30

X = (76×30)/19

X = 120 minutes

it will take the clowns 120 minutes working together to have 76 balloons.