Question

a bouquet of balloons contains red, purple, and orange balloons. the table shows how many balloons of each color are in the bouquet.

color	number
orange	p - 1
purple	p

if p is the number of purple balloons in a bouquet that has a total of 17 balloons, how many purple balloons are there?

Explanation:

Step1: Set up the equation

The total number of balloons is the sum of red, orange, and purple balloons. So, \(4p+(p - 1)+p=17\).

Step2: Simplify the left - hand side

Combine like terms: \(4p + p-1 + p=(4p + p + p)-1=6p-1\). So the equation becomes \(6p - 1 = 17\).

Step3: Solve for p

Add 1 to both sides of the equation: \(6p-1 + 1=17 + 1\), which gives \(6p=18\). Then divide both sides by 6: \(p=\frac{18}{6}=3\).

Answer:

3