Question

Marcia bought a bag of red white and blue balloons for the party there were 49 balloons in the bag if there are twice as many red as blue and half as many white as blue how many of each color are in the bag?

Answer 1

There are 28 red, 7 white and 14 blue balloons in the bag.

Explanation:

Given,

Total number of balloons = 49

Solution,

Let the number of red balloons be 'r'.

Let the number of white balloons be 'w'.

And also let the number of blue balloons be 'b'.

The total number of balloons is the sum of the number of red balloons, the number of white balloons and the number of blue balloons.

On framing in equation form, we get;

`r+w+b=49\ \ \ \ \ equation\ 1`

Now according to question, there are twice as many red as blue.

So we can frame it as;

`r=2b\ \ \ \ \ \ equation\ 2`

Again according to question, there are half as many white as blue.

So we can frame it as;

`w=(1)/(2)b\ \ \ \ \ equation\ 3`

Now we substitute the values from equation 2 and equation in equation 1, and get;

`2b+(1)/(2)b+b=49`

Now we add the fraction by making the denominator equal;

`(2*2)/(2)b+(1)/(2) b+(2)/(2)b=49\\ \\(7)/(2)b=49`

Now multiplying both side by '2' using multiplication property, we get;

`(7)/(2)b*2=49*2\\\\7b=98`

Now dividing both side by '7' using division property, we get;

`(7b)/(7)=(98)/(7)\\\\b=14`

On substituting the value of 'b' in equation 2, we get;

`r=2b=2*14=28`

Again on substituting the value of 'b' in equation 3, we get;

`w=(1)/(2)b=(1)/(2)*14=7`

Hence There are 28 red, 7 white and 14 blue balloons in the bag.

Answer 2

Red color= 28 balloon

Blue color= 14 balloon

White color= 7 balloon

Explanation:

Given: There are 49 balloons

As given, there are 2 red balloon equal to the number of blue balloon

∴
`2 red= blue\ balloon`

Again given, there are 1/2 white balloon equal to the number of blue balloon.

∴
`(1)/(2) \ white= blue\ balloon`

As above equation, we can understand that:

`2\ red= (1)/(2) \ white\ balloon`

multiplying both side by 2

⇒
`4\ red= white\ balloon`

which mean, if we have 2 blue balloon then we will have 4 red and 1 white balloon.

∴ Total combination of all color of balloon=
`2+4+1= 7`

Now, checking how many number of times combination can we have in 49 balloon.

`(49)/(7)= 7 \ times`

Next, finding number of balloon in each color.

Red color=
`4* 7= 28\ balloon`

Blues color=
`2* 7= 14\ balloon`

White color=
`1* 7= 7\ balloon`