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

[tex]\begin{array}{l}
P( ext { Luna winning })=\frac{ ext { Number of tickets purchased }}{ ext { Total number of tickets sold }} \
20 \%=\frac{20}{x} \
\frac{1}{5}=\frac{20}{x} \
x=69\
\end{array}[/tex]

Question

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

[tex]\begin{array}{l}
P(	ext { Luna winning })=\frac{	ext { Number of tickets purchased }}{	ext { Total number of tickets sold }} \
20 \%=\frac{20}{x} \
\frac{1}{5}=\frac{20}{x} \
x=69\
\end{array}[/tex]

GinnyAnswer · Answer

Define x as the total tickets sold. 
 Express Luna's winning probability: x 20 ​ = 20% = 5 1 ​ . 
 Solve for x : x = 20 ⋅ 5 . 
 The total number of tickets sold is 100 ​ . 
 
 Explanation 
 
 Analyze the problem Let's analyze the problem. Luna bought 20 tickets, and this gives her a 20% chance of winning the raffle. We need to find the total number of tickets sold. 
 
 Express the probability Let x be the total number of tickets sold. The probability of Luna winning is the number of tickets she purchased divided by the total number of tickets sold. So, we have: P ( Luna winning ) = Total number of tickets sold Number of tickets Luna purchased ​ = x 20 ​ We are given that Luna's probability of winning is 20%, which can be written as a fraction: 20% = 100 20 ​ = 5 1 ​ 
 
 Solve for x Now, we set up the equation: 5 1 ​ = x 20 ​ To solve for x , we can cross-multiply: 1 ⋅ x = 5 ⋅ 20 x = 100 
 
 State the final answer Therefore, the total number of tickets sold in the raffle is 100.

Examples 
 Imagine you're organizing a school raffle to raise money for a class trip. You know that each student who participates has a certain number of tickets, and you want to figure out how many tickets you need to sell in total to reach your fundraising goal. This problem helps you understand the relationship between individual ticket purchases, the probability of winning, and the total number of tickets sold, allowing you to plan your raffle effectively. For example, if each student buys 5 tickets and you want their chance of winning to be 1 in 50, you can calculate the total number of tickets you need to sell.

Anonymous · Answer

Luna's winning probability can be expressed as the number of tickets she purchased divided by the total number sold. By setting up the equation x 20 ​ = 5 1 ​ and solving for x , we find that the total number of tickets sold is 100. Therefore, the answer is 100 ​ . 
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Answer (2)

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