Question

For a party in kindergarten balloons of three colors were bought: red, green, and yellow. There were 40 red balloons, the number of green balloons made up 3/5 of the number of red balloons and 2/3 of the number of yellow balloons. How many balloons were brought to the kindergarten? What part of them could be blown up, if before the blowing-up 1/20 of the red balloons, 1/12 of the green balloons, and 1/36 of the yellow balloons popped?

Answer 1

Answer:

Total number of balloons is, 100

Part of them could be blown up , $\frac{19}{20}$

Step-by-step explanation:

Let the number of red balloons be x , number of green balloons be y and the number of yellow balloons be z respectively.

Given: Number of red balloons x = 40

y = $\frac{3}{5}x$ = $\frac{3}{5}\times 40=3 \times 8= 24$

and

$y = \frac{2}{3} z$

Multiply both sides by $\frac{3}{2}$;

$\frac{3}{2} y = \frac{2}{3} z \times\frac{3}{2}$

Simplify:

$z = \frac{3}{2} y$

Substitute the value of y = 24 to solve for z;

$z = \frac{3}{2} \times 24 = 3 \times 12 = 36$

Therefore, total number of balloons = x+y+z = 40+24+36 = 100 balloons.

Number of balloons popped = $\frac{1}{20}x + \frac{1}{12} y + \frac{1}{36} z$

Substitute the value of x, y and z we get;

Number of balloons popped = $\frac{1}{20} \times 40 + \frac{1}{12} \times 24 + \frac{1}{36} \times 36$ = 2+2+1 = 5

The number of balloons popped is  5.

Number of balloon that can be blown up = total number of balloon -number of balloons popped =  100 - 5 = 95.

The part of the balloons could be blown up is; $\frac{95}{100} = \frac{19}{20}$