Luna entered a raffle for a new pair of running shoes. She purchased 20 tickets and was told that she had a 29% chance of winning. How many tickets were sold?

[tex]\begin{aligned}
ext { P(Luna winning) } & =\frac{ ext { Number of tickets purchased }}{ ext { Total number of tickets sold }} \
20 \% & =\frac{29}{x} \
\frac{1}{5} & =\frac{29}{x} \
x & =\frac{1}{x} ext { tickets }
\end{aligned}[/tex]

Question

Luna entered a raffle for a new pair of running shoes. She purchased 20 tickets and was told that she had a 29% chance of winning. How many tickets were sold?

[tex]\begin{aligned}
	ext { P(Luna winning) } & =\frac{	ext { Number of tickets purchased }}{	ext { Total number of tickets sold }} \
20 \% & =\frac{29}{x} \
\frac{1}{5} & =\frac{29}{x} \
x & =\frac{1}{x} 	ext { tickets }
\end{aligned}[/tex]

GinnyAnswer · Answer

Let x be the total number of tickets sold. 
 Set up the equation: x 20 ​ = 0.29 . 
 Solve for x : x = 0.29 20 ​ ≈ 68.9655 . 
 Round to the nearest whole number: x = 69 . The total number of tickets sold is 69 ​ . 
 
 Explanation 
 
 Analyze the problem Let's analyze the problem. Luna bought 20 tickets and has a 29% chance of winning. We need to find the total number of tickets sold. The probability of winning is the number of tickets Luna purchased divided by the total number of tickets sold. 
 
 Set up the equation Let x be the total number of tickets sold. The probability of Luna winning is x 20 ​ . We are given that this probability is 29%, which can be written as 0.29. 
 
 Formulate the equation Now we set up the equation: x 20 ​ = 0.29 
 
 Solve for x To solve for x , we multiply both sides by x and then divide by 0.29: x = 0.29 20 ​ 
 
 Calculate x Calculating the value of x : x = 0.29 20 ​ ≈ 68.9655 
 
 Round to the nearest whole number Since the number of tickets must be a whole number, we round x to the nearest whole number, which is 69. 
 
 State the final answer Therefore, the total number of tickets sold is approximately 69.

Examples 
 Imagine you are organizing a raffle to raise money for a charity. You sell tickets for $1 each, and you know that you want to give away a prize that is worth $50. You also know that you want to have a 29% chance of winning the prize. This calculation helps you determine how many tickets you need to sell to make a profit and still offer a reasonable chance of winning.

Anonymous · Answer

Luna purchased 20 tickets and had a 29% chance of winning. By setting up the equation x 20 ​ = 0.29 and solving for x , we find that the total number of tickets sold is approximately 69. Thus, the total tickets sold in the raffle is about 69. 
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Answer (2)

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