An angel came in her dream
Tanya ran a lemonade stand last year at the Little League baseball playoff games at the New Village Park. She made good money. So she thought of doing it again on the coming Saturday and Sunday.
On the Tuesday before the games, Tanya played all day, fell asleep and started to dream. An angel came in her dream. The angel was beautiful. She had a large tiara made of gold. Twinkles in her eyes matched the rhinestones on her dress. The angel was singing a song and dancing. After waking up, Tanya tried to think of the angel’s song. She couldn’t get the words. She thought that the angel had something round which could be cut. After the round thing was cut, it became money. It didn’t make any sense. She started watching TV where she saw a commercial for Pete’s Pizza. It was something round and could be cut but the pieces didn’t become money! Tanya thought harder about it. She could sell pizza slices and make money. That’s what the angel must have been saying, “Sell pizza slices at the lemonade stand.” Now, that made sense to Tanya.
Taking mom’s permission
Tanya to her mom: You know that I am going to sell lemonade at the New Village Park on the coming weekend. I want to sell pizza too.
Mom: What’s this craze now? You did well with the lemonade stand last year. Why mess it up by adding pizza?
Tanya: I want to try something different for fun. I will have Tinku help me. Let me try it, please.
Mom agreed but on the condition that Tanya had to keep a record of all expenses, income and profits not just in actual dollars but also in fractions and percentages. Tanya realized that mom wouldn’t give the permission without it. So, she accepted.
The lemonade part of the business was not new. She could repeat what she had done the last year. She knew that she had to buy about $55 worth of supplies for it. It was all set but she had to think about the pizza business.
Tanya went to Pete’s Pizza
Tanya went to Pete’s Pizza. She had a chat with the owner Mr. Pete Valenti. She told him about her plan. She asked about different pizzas.
Pete: We have medium size pizzas with 8 slices and large with 10. We also have rectangular party pizzas with 20 slices.
Tanya: Are the slices from different pizzas the same size.
Pete: They are very similar.
Tanya: How much do the pizzas cost?
Pete: The prices for the common three topping pizzas are $10 for the medium, $12 for the large and $24 for the party size. More toppings and special pizzas cost extra.
Tanya: What discount will you give me? I want to sell the pizzas by the slice. This way many people will get to try your pizza.
Pete: I can give you a 10 % discount. That’s all I can afford.
Tanya: I know that you send flyers advertising your pizzas. That must cost you money. What if I gave your flyers away at the park?
Pete: How many people do you expect to come to your stand?
Tanya: Last year, I sold 400 glasses of lemonade on the two days. I hope it will be the same this year.
Pete: Okay. I will give you a total of 20 % discount if you give out 200 flyers.
Tanya: Can you deliver the pizzas to the New Village Park on Saturday and Sunday?
Pete: Yes, but it will be $2.50 extra for each delivery.
Tanya: Can you give me free delivery? I will order the pizzas on two days. I will buy pizzas worth of a total of 60 slices.
Pete: No, but I will make the total discount to 30 % if you order a total of 60 slices or more.
Tanya: Thanks. I will figure out which pizzas and then contact you.
Medium, large or party pizza?
First, Tanya tried to figure what pizza would give her the cheapest slices. At this time she did not want to think of the rebate. She left that for later.
A medium pizza had 8 slices and cost $10. One slice of this would be 1/8th of the pizza. The cost per slice would be $10/8 which came to $1.25.
The large pizza had 10 slices and cost $12. One slice of this would be 1/10th of the pizza. The cost of one slice would be $12/10 which came to $1.20.
The party pizza had 20 slices and cost $24. One slice of this would be 1/20th of the pizza. The cost of one slice would be $24/20 which came to $1.20.
Thus the prize per slice was higher for the medium size pizza but it was the same for the large or the party size pizza. Party pizza slices would be squares. The large pizza was round and its slices looked more like pizza slices. So she decided to buy the large pizzas.
Cost of the 60 pizza slices
For 60 slices, there was a 30 % discount. That meant that 3/10th of all the slices would be free. She would have to pay only for 7/10th (1-3/10 = 7/10) of the slices. She figured 60 x 7/10 = 42. That meant that she would have to pay only for 42 slices at the rate of $1.20/slice. That came to a total of $50.24. She also calculated that 30 % of $1.20 was 36 cents. So she would have to pay $1.2 x 60 – $0.36 x 60 which came to $50.24. She was happy that she got the same answer in two different ways.
So she decided to order 6 large pizzas: 3 for each of the two days. On each day, she would get a pepperoni pizza, a ham and pineapple pizza and a vegetarian pizza. The delivery added a cost of 2 x $2.5 or $5. The pizza cost now became $50.24 + $5 = $55.24. She would also need small paper plates and serviettes. She added $2.76 for them. The total now came to $55.24 + $2.76 = $58. This is what she would spend on the pizza business.
The lemonade and pizza stand on the first day
Tanya called Tinku and reminded him about the money he had made last year. She asked Tinku if he wanted to work again. Tinku agreed happily. Tanya rented a big table from the park. She would have carry it from the store room and bring it back each day. She would also have to pay $10 for it.
On the table, they had the cooler, the jars for the lemonade, the place for the pizzas, the glasses, the plates, the serviettes and the flyers from Pete’s Pizza. They put up a big sign “Lemonade 25 cents. Pizza slice with free lemonade: $2.00.” Actually, it came to a pizza slice for $1.75 plus the 25 cents for the lemonade.
At about 11 O’clock, it began to get hot. Players, coaches, volunteers and others began to trickle in to buy the lemonade. Some of them asked about the pizza. They were told that they could buy it fresh at 12 O’clock. They were also given a flyer for Pete’s Pizza.
Finally, the pizzas arrived at noon. Already, there was a short line formed at the stand. Some people came for lemonade alone and the others for pizza and lemonade. Tanya and Tinku both had to work hard. Then, fewer people were coming.
At one time Tanya thought that she might not sell all the pizza slices. Suddenly, a baseball game finished. A short line formed again. This is how it worked. Very few customers would come for a while. Then short lines would form after a game finished.
At 2 O’clock, Tanya took a sigh of relief. Only two slices of pizzas were left. By this time she was also hungry. She gave one slice to Tinku and gobbled up the other one.
By 4 O’clock, they ran out of lemonade too. They put the waste in the garbage and the table in the room at the park.
The same thing happened on Sunday.
They started at 10. The pizzas came at noon and finished around 2 O’clock. This included the two slices for Tanya and Tinku. It was a hotter day. So the lemonade was gone by 3. They winded up like the previous day and went home.
Tanya did the counting.
She had sold 56 slices of pizzas because Tanya and Tinku ate the other 4. At $1.75/slice, this was a $98. She had also sold a total of 400 glasses of lemonade.
This is included those sold with the pizza slices. At 25 cents each the 400 glasses of lemonade gave a total of $100. She counted and indeed have $198 left.
Tinku had made only $5 last year when they sold lemonade. This year he had worked much harder. So Tanya gave him $15. Tinku was very happy with this increase in earnings. Before Tanya could calculate her profits, she remembered all the expenses. They were $55 for the lemonade supplies, 58 for the pizzas and supplies, 10 for the table and 15 for Tinku.
She also had to prepare the report for mom.
| Amount | Fractional amount | Percent amount | |
| Expenses | |||
| Tinku’s pay | $15 | 15/138= 5/46 | 15/138×100=10.87% |
| Table rental | $10 | 10/138= 5/69 | 10/138×100=7.25% |
| Lemonade related supplies | $55 | 55/138= 55/138 | 55/138×100=39.86% |
| Pizza related supplies | $58 | 58/138= 29/69 | 58/138×100=42.03% |
| Total expenses | $138 | (15+10+55+58)/138=1 | 10.87+7.25+39.86+42.03=100% |
| Income | |||
| Lemonade | $100 | 100/198=50/99 | 100/198×100=50.51% |
| Pizza slices | $98 | 98/198=49/99 | 98/198×100=49.49% |
| Total income | $198 | +(50+49)/99=1 | 60.51+49.49 =100% |
| Profit | $60 | ||
| Profit as fraction of the expenses | 60/138=10/23 | ||
| Profit as percent of expenses | 60/138×100=43.48 |
Mom was happy with the report. Tanya had written all expenses, income and profit. She was happy the way Tanya had calculated the fractions and the percentages.
Tanya was happy that she made more money than the last year. Still, she was thinking of lot of things.
Should she have done the pizza business or stuck to the lemonade alone?
Should she have bought more pizzas to make bigger profit? If so, how many more? She remembered the risk of buying more than she could sell.
What do you think?
Math Stories For You 