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Exploration: System of Equations

Last updated over 2 years ago
10 questions
For your summer break, you get a paid internship at a famous drama production. The production lasts 2 months and the pay you get is of two types. For every day you work on set you to get paid a little more than when you work from home to compensate for transportation and food.
In the first month, you get paid a total of $1060 for working 12 days on set and 10 from home.
In the second month, you spend 20 days on set and only 5 at home and earn a total of $1300.
What did they agree to pay you for on set days and for work-from-home days?
1

The first paragraph sets the context for the word problem. The most important task, ALWAYS, is to figure out what the variables are, the unknown quantity. The clue is almost always in the last sentence. Make your guesses!
1. How many variables are there?
2. What are they?
3. Assign alphabets (lowercase) to the variables.

1

Now, month one is just situation 1 in disguise.
Try to create a math statement out of the month 1 statement.

1

Use DESMOS Graphing Calculator to plot the above statement.
Discuss:
1. What makes a graph linear?
2. What is the meaning of solution?
3. What are some possible values for your variables?
4. Is there any way to narrow down the exact value?

1

Now, convert month 2 (situation 2) into a math statement.
Lesson: These kind of linear equations are called a system of linear equations because they share the same variable.

1

Without deleting the old graph, plot the second equation on DESMOS.
Discuss:
1. What do you observe?
2. What is the meaning what you observe? Will it count as a solution?

1

In your own wordsm describe the significance of the point of intersection.

1

Finally, what is the answer to the question? How was the pay divided?

Try the following question yourself.

When shopping for notebooks, you buy 3 hardbound notebooks and 5 paperback notebooks. It ends up being a total of ₹650.
Your sibling buys 5 hard-bound notebooks and 10 paperback notebooks (greedy child!) and ends up paying ₹1200.
What was the price of the hardbound and the paperback notebooks, respectively?
1

Solve the above question using the steps given above.

The knitting club sold 40 scarves and hats at a winter festival and made $700 from the sales. They charged $18 for each scarf and $14 for each hat.
1

If s represents the number of scarves sold and h represents the number of hats sold, which system of equations represents the constraints in this situation?

1

Find the number of hats and scarves sold.