Introducing Sara and her Nana
Vijay and Sonia met in college in India, married and then moved to North America. Here, they worked as software experts in a large company. Life was difficult in the beginning but they worked hard and settled well.
Shanti is Vijay’s mother. She lived in India and wanted them to give her a grandchild. She kept asking them every time they talked to her. Vijay and Sonia told Shanti that both of them worked full time and also took care of cooking, laundry and all the chores at home. Therefore, they did not have enough time to raise a child. In India one can get maids to do such house work. Therefore, Shanti had hard time understanding all this. Finally, they all agreed to the solution that Shanti would come and live with them. Within a year after the arrival of Shanti, Sonia gave birth to a daughter. Shanti was thrilled. She wanted to name her granddaughter Sarasvati after the goddess of knowledge. Sonia objected by saying that people here would have difficulty remembering and pronouncing that name. Shanti did not give up. She convinced them that they could name their new baby Sarasvati and call her Sara for short.
Sara and Nana had daily chitchats
Vijay and Sonia continued working full time. Sara was practically raised by Shanti. She called her “Nana” ever since she could say her first words. Every day, Sara would come home from school and tell Nana everything and nothing. Nana enjoyed this chitchat with the little one.
One day Sara came home from school and told Nana that she had started to learn algebra. It came out during their conversation that Shanti had never learned algebra. Sara thought that she could do something about it.
Sara: Nana, algebra is easy. I will teach you but first you have to tell me something.
Shanti: What do I have to tell you? I will, if I know the answer to your question.
Sara: Remember, you said that you would buy my little brother a xylophone and get me a yoyo. I want a big red yoyo.
Shanti: Yes, you and I will go together to the toy store this weekend, and I will buy the two toys as promised. You can choose a yoyo of any size and color.
Costs of xylophones and yoyos
Sara: No. that was not the question. The real question is a little harder. If you answer this question, I will teach you algebra: “Suppose that two xylophones and one yoyo cost $26 and that one xylophone along with three yoyos costs $18, how much does a yoyo cost?”
Shanti did not learn algebra at school but was really smart with numbers. She thought for a while and then said with a big smile: The yoyo costs $2. If that’s correct, you have to teach me algebra now. Don’t you?
Sara: But Nana, how did you figure that out?
Nana: Look, you said that one xylophone and three yoyos cost $18 and that means two xylophones and six yoyos would be $36. You also told me that two xylophones and one yoyo cost $26. The difference between the two is $10 and that must be the price of five yoyos. So, one yoyo would be $2.
Sara: Love you Nana. Give me hug. You did it right, and that means you already know algebra.
Shanti: How so?
Writing x for xylophone and y for yoyo
Sara: Okay, the word xylophone starts with the letter x and the word yoyo starts with the letter y. So I can just write x and y for them and then tell you what you did.
Sara proceeded to write out for Nana what she had meant:
2 x + y = 26, and
x + 3 y = 18.
Shanti: I get that.
Sara: then you multiplied both sides of the equation x + 3 y = 18 by 2 to get
2x + 6y = 36
From this you subtracted 2x + y = 26.
This got rid of x or as my math teacher would say, “it eliminated x to give you 5 y =10.”
Dividing both sides by 5 you got y =2.
That’s how you got the price the yoyo. From this you would also get that xylophone costs $12.
Shanti: Is that it, you just write x and y instead of the words xylophone and yoyo, and then call it algebra?
Sara: That’s the start. Our math teacher taught us other ways of solving these equations too.
Why write x and y?
Shanti: But why write x and y?
Sara: The problem would have remained the same if instead of xylophone and yoyo, x and y were a Barbie and a truck. You would solve it the same way. It could be aeroplanes and cars, the prices could be different but we could still write and solve the equations the same way.
Shanti was starting to understand and said: Okay, Sara that was good. I love you my algebra teacher.
Challenge
Sara’s real name is Sarasvati. If we were to say that it has x consonants, y vowels, and the total number of letters in her name was t, then we can write any of these equations:
x = 5, y = 4, x + y = 9 or t = 9, t-x = 4. Write your first and last names together and then complete the following x =_, y =_, x+y =_, t =_, t-x =_. What value did you get for t – x? What did this value mean for you? Was it the number of vowels in your name?
No solution provided for this challenge because it depends on your name. Just follow the given example.
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