Question

428 Mdm Yati bought some red and blue balloons for a party, of theballoons were red. Half of the red balloons and of the blue balloonsburst..​ What fraction of the balloons were left in the end?

Answer 1

`\( (9)/(16) \)` of the balloons were left in the end after half of the red balloons and a quarter of the blue balloons burst.

Step-by-step explanation:

Let's denote the total number of balloons as
`\( T \)`. Mdm Yati bought some red balloons, and the number of red balloons is given as
`\( (3)/(4) \)` of the total
`(\( (3)/(4) * T \))`, and the number of blue balloons is
`\( (1)/(4) \)` of the total
`(\( (1)/(4) * T \))`.

Now, half of the red balloons burst, which means
`\( (1)/(2) \) of \( (3)/(4) * T \)` balloons burst. Similarly,
`\( (1)/(4) \)` of the blue balloons burst.

The remaining fraction of red balloons is
`\( (1)/(2) * (3)/(4) \)` of the total, and the remaining fraction of blue balloons is
`\( (3)/(4) * (1)/(4) \)` of the total.

Now, let's find the total fraction of balloons left:

`\[ \text{Total fraction left} = \text{Remaining fraction of red balloons} + \text{Remaining fraction of blue balloons} \]`

`\[ = (1)/(2) * (3)/(4) + (3)/(4) * (1)/(4) \]`

`\[ = (3)/(8) + (3)/(16) \]`

`\[ = (6)/(16) + (3)/(16) \]`

`\[ = (9)/(16) \]`

So,
`\( (9)/(16) \)` of the balloons were left in the end.