Question

Lin’s uncle is opening a bakery. On the bakery’s grand opening day, he plans to give away prizes to the first 50 customers that enter the shop. Every fifth customer will get a free bagel. Every ninth customer will get a free blueberry muffin. Every 12th customer will get a free slice of carrot cake.

1. Diego is waiting in line and is the 23rd customer. He thinks that he should get farther back in line in order to get a prize. Is he right? If so, how far back should he go to get at least one prize? Explain your reasoning.

2. Jada is the 36th customer.

a. Will she get a prize? If so, what prize will she get?

b. Is it possible for her to get more than one prize? How do you know? Explain your reasoning.

3. How many prizes total will Lin’s uncle give away? Explain your reasoning.

Answer 1

1. Yes, 1 position backwards

2. Yes, a free blueberry muffin and a free slice of carrot cake

b. Yes

3. 19 prizes

Explanation:

The given conditions for winning a prize are as follows;

The prize that every 5th customer gets = A free bagel

The prize that every 9th customer gets = A free blueberry muffin

The prize that every 12th customer gets = A free slice of carrot cake

Therefore, the prizes will go to the 5th, 9th, 10th, 12th, 15th, 18th, 20th, 24th, 25th, 27th, 30th, 35th, 36th, 40th, 45th, 48th, and 50th positon customers

1. Diego being 23rd is right for thinking that he should get farther back in line in order to get a prize

He should get one position behind to 24th position

The reason is because prizes will be given to every 12th customer, and the 24th customer is the second 12th customer

2. Yes Jada will get a price as her position corresponds to the consecutive 9th and 12th customers position

Jada will get a free blueberry muffin and a free slice of carrot cake

b. It is possible for Jada to get more than one prize

This is so because her position coincides with the consecutive 9th and 12th customers position

3. The number prizes that Lin's uncle gives away are;

5th, 9th, 10th, 12th, 15th, 18th, 20th, 24th, 25th, 27th, 30th, 35th, 36th, 40th, 45th, 48th, and 50th = 17 prizes

including 1 extra prize each for the 36th and 45th customers which gives a total of 19 prizes.