Question

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

Answer 1

The number of balloons is:

• Red balloons = 28
• Blue balloons = 14
• White balloons = 7

Explanation:

First, we establish the variables:

• R = Number of red balloons.
• B = Number of blue balloons.
• W = Number of white balloons.

Now, we establish the equations with the information given in the exercise:

1. R + B + W = 49
2. R = 2B
3. B = 2W or W = 1/2B

We replace the equation 2 in the equation 1:

• R + B + W = 49
• (2B) + B + W = 49
• 3B + W = 49

In this moment, we replace the equation 3 in the las equation obtained:

• 3B + W = 49
• 3*(2W) + W = 49
• 6W + W = 49
• 7W = 49

We solve the variable W:

• 7W = 49
• W = 49/7
• W = 7

Now we know the number of white balloons is 7, we replace this value in the third equation to know the number of blue balloons:

• B = 2W
• B = 2 * (7)
• B = 14

In the end, we replace this last value in the second equation to calculate the number of red balloons:

• R = 2B
• R = 2 * (14)
• R = 28

In this forms, we know the number of balloons is: 28 red, 14 blue, and 7 white.