Tanya’s ambition
Tanya heard that the Little League baseball playoff games for the region were in the New Village Park. The park was only 200 meters away from her home. The games would be on Saturday and Sunday from 10 am to 5 pm. Tanya thought that she could make big money if she ran a lemonade stand in the park for these two days. There would be lots of players and their parents, coaches and other volunteers. She figured she could sell a small glass of lemonade for a quarter ($1/4 or 25 cents) and selling 400 glasses she could make 400 times $1/4 which equals $100.
There were lots of hurdles in her plan – convincing mom, buying supplies, carrying large amount of lemonade to the Park. Tanya managed to convince mom and also decided to hire Tinku.
Mom: How much money do you need for the supplies?
Tanya’s strategy
Tanya: I figured that 10 cents ($1/10) of lemonade powder with sugar will make 1 small glass of good lemonade. 1 small glass is 1/400 fraction of 400 glasses. So I will need 400 times $1/10 which comes to $40.
Mom: A small glass of lemonade is about 200 milliliters or 1/5th of one liter, 400 glasses would be 400 times 1/5 which is 80 liters. How are you going to carry such heavy jars?
Tanya: Mom, it will be only 40 liters on each day. I have a plan.
They bought $40 worth of lemonade powder, and spent another $15 on disposable glasses some garbage bags. Mom told Tanya that this total of $55 they spent on the supplies was a loan.
Juice Jar, Serving Jar and Water Jar
Tanya took three jars and named them: Juice Jar, Serving Jar and Water Jar.
The Juice Jar could hold 4 litres. She had decided to sell a total of 400 glasses in two days. So on the first day she would sell 1/2 of the 400 which was 200 glasses. She put the lemonade powder for 200 glasses in the Juice Jar and dissolved it in 4 litres of water. The lemonade to be served on that day would be 1/5 litres per glass times 200 which is 40 litres. The volume of the Juice Jar (4 litres) was 1/10th of 40 litres. She would take one part of this juice and mix it with 9 parts of water. She would do this using the Serving Jar.
The Serving Jar was a 2 litre container. She knew that one glass would hold 1/5th of a litre (200 ml). She took a glass of the concentrated lemonade from the Juice Jar and 9 x 1/5 litres of water. That made to 2000 ml (2 litres) to serve 10 glasses of lemonade.
Tinku’s job
Tanya also had a third Jar called the Water Jar (4 litres). She gave it to Tinku and told him that every time they needed water, he would fill it from the tap and bring it to the lemonade stand. For each water trip Tinku would get a quarter (25 cents).
Tanya found a large tree and set up her stand in its shade. She had the cooler. She also used the cooler as a table on which she put her serving jar and some glasses. On one side, she also had a garbage bag for people to throw away the empty glasses.
Players and parents started to drop in. Tanya would pour a glass of lemonade from the Serving Jar and hand it over to them for a quarter (25 cents). When the Serving Jar became empty, she refilled it with water and a glassful of the concentrated lemonade from the Juice Jar. When the Water Jar became empty, Tinku refilled it. One glass at a time, Tanya sold all the lemonade that she had. Tinku asked Tanya if he could come the next day too. Of course, Tanya agreed.
Who made how much money?
The same thing happened on Sunday.
In the two days, Tinku had made a total of 20 trips each time carrying 4 litres of water. Thus he had carried a total of 80 litres of water. He was to be paid a quarter (25 cents or $1/4) for each trip So they calculated that Tinku had earned 20 times $1/4 or a total of $5. Tanya gave him the money.
How much money did they get from selling the lemondate? Over the two days they had sold 400 glasses charging $1/4 for each glass. That would come out to 400 x $1/4 or $100.
How much money did Tanya spend? She spent $55 on supplies and gave $5 to Tinku. So that was a total of $60.
How much money did the smart girl make? Take away $60 from $100. That left Tanya with a profit of $40.
Tinku: That’s a lot more than what I made.
Tanya: But I took all the risk and did most of the work.
Tinku: That’s true. I am glad we did this.
Now, mom knew that she made the right decision because Tanya was a go-getter.
Challenge
Peter says that he can sip a whole 2 liter bottle of coke. Tinku brags that he can sip 500 milliliters. Tanya asks Tinku why he is bragging because 1 millilitre is only 1/1000 of a liter. What do you think?
Solution: Peter can sip 2 liters which is 2000 ml. Tinku has nothing to brag about because 2000 ml is 4 times what he can sip which is 500 ml.
Supplementary
Tanya just came back from a running camp and is talking to her friend Tinku.
Tinku: Welcome back Tanya. Tell me something interesting about the camp.
Tanya: You will love the running program I was in. It was a 7 day thing. The day 1, I ran half a kilometer. It was easy. On day 2, they made me run one third kilometer more than day 1, on the day 3, it was one fourth kilometer more than day 2.
Tinku: Let me guess, on day 4, it was one fifth kilometer more than day 3, on day 5, one sixth kilometer more than day 4, on day 6, one seventh kilometer more.
Tanya: It was a lot of running. On day 7, it was one eighth kilometer more than day 6. I don’t believe it. I could still run.
Tinku: You know, I love all the details. I want to figure out how much you ran on day 7.
| Day | From day before | Add km | Total km |
| 1 | 0 | 1/2 | 0+1/2= 1/2 |
| 2 | 1/2 | 1/3 | 3/6+2/6= 5/6 |
| 3 | 5/6 | 1/4 | 10/12 +3/12 =13/12 |
| 4 | 13/12 | 1/5 | 65/60 + 12/60 = 77/60 |
| 5 | 77/60 | 1/6 | 77/60 + 10/60 = 87/60 |
| 6 | 87/60 | 1/7 | 609/420 +60/420 = 669/420 |
| 7 | 669/420 | 1/8 | 1338/840+105/840=1443/840 |
Tanya: As you can see, I ran 1313/840 on day 7. It was more than three times on day 1 (3×1/2 = 3 x 420/840= 1260/840).
Math Stories For You 