Podcast
Questions and Answers
Which of these ordered pairs are not points on the graph of $2x + 4y = 20$? Justify your decision.
Which of these ordered pairs are not points on the graph of $2x + 4y = 20$? Justify your decision.
How many muffins and doughnuts can Jacob buy with $15 if muffins are 75¢ each and doughnuts are 25¢ each?
How many muffins and doughnuts can Jacob buy with $15 if muffins are 75¢ each and doughnuts are 25¢ each?
Various combinations of 0-20 muffins and 0-60 doughnuts depending on allocation of budget.
What is the maximum number of muffins that Jacob can buy?
What is the maximum number of muffins that Jacob can buy?
20
What is the maximum number of doughnuts that Jacob can buy?
What is the maximum number of doughnuts that Jacob can buy?
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Write an equation that describes Jacob's options for buying muffins and doughnuts.
Write an equation that describes Jacob's options for buying muffins and doughnuts.
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Which representation do you think is more useful for Jacob, a graph or a table? Justify your choice.
Which representation do you think is more useful for Jacob, a graph or a table? Justify your choice.
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State two ordered pairs that satisfy the linear relation $y = 5x - 1$ and one ordered pair that does not.
State two ordered pairs that satisfy the linear relation $y = 5x - 1$ and one ordered pair that does not.
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State two ordered pairs that satisfy the linear relation $3x - 4y = 24$ and one ordered pair that does not.
State two ordered pairs that satisfy the linear relation $3x - 4y = 24$ and one ordered pair that does not.
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State two ordered pairs that satisfy the linear relation $y = -25x + 10$ and one ordered pair that does not.
State two ordered pairs that satisfy the linear relation $y = -25x + 10$ and one ordered pair that does not.
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State two ordered pairs that satisfy the linear relation $5x = 30 - 2y$ and one ordered pair that does not.
State two ordered pairs that satisfy the linear relation $5x = 30 - 2y$ and one ordered pair that does not.
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Define suitable variables for Caroline's working hours equation.
Define suitable variables for Caroline's working hours equation.
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Define suitable variables and write an equation for Caroline's earnings.
Define suitable variables and write an equation for Caroline's earnings.
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Define variables and write an equation for Justin's weekly earnings.
Define variables and write an equation for Justin's weekly earnings.
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Define variables and write an equation for Justin's new job offer.
Define variables and write an equation for Justin's new job offer.
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Define suitable variables and write an equation for the piggy bank situation.
Define suitable variables and write an equation for the piggy bank situation.
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Graph the relations in question 5, parts a) and b).
Graph the relations in question 5, parts a) and b).
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Should Justin take the new job if he usually has about $18,000 in weekly sales?
Should Justin take the new job if he usually has about $18,000 in weekly sales?
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Create a table to show Deb's spending on calls and text messages.
Create a table to show Deb's spending on calls and text messages.
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Create a graph representing Deb's potential spending on calls and text messages.
Create a graph representing Deb's potential spending on calls and text messages.
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Create an equation for Leah's monthly paycheck based on sales.
Create an equation for Leah's monthly paycheck based on sales.
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Is Leah's pay before deductions of $4566.09 correct given her sales of $96,174?
Is Leah's pay before deductions of $4566.09 correct given her sales of $96,174?
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Study Notes
Checking Understanding
- Evaluate which ordered pairs satisfy the linear equation 2x + 4y = 20.
- Ordered pairs in question:
- (10, 0)
- (-3, 7)
- (6, 2)
- (0, 5)
- (12, -1)
Representing Linear Relations
- Jacob's budget for muffins and doughnuts is $15.
- Muffins cost 0.75each,anddoughnutscost0.75 each, and doughnuts cost 0.75each,anddoughnutscost0.25 each.
- Possible combinations of muffins (x) and doughnuts (y) derive from the equation: 0.75x + 0.25y ≤ 15.
- Maximum muffins Jacob can buy: 20 (if he buys muffins only).
- Maximum doughnuts Jacob can buy: 60 (if he buys doughnuts only).
- Graphing options can visually represent combinations possible within the budget.
Practising Linear Relations
- Find two ordered pairs for each linear equation:
- y = 5x - 1
- Satisfying pairs: (0, -1), (1, 4)
- Non-satisfying pair: (2, 5)
- 3x - 4y = 24
- Satisfying pairs: (4, 0), (8, 6)
- Non-satisfying pair: (0, 6)
- y = -25x + 10
- Satisfying pairs: (0, 10), (1, -15)
- Non-satisfying pair: (0, 20)
- 5x = 30 - 2y
- Satisfying pairs: (6, 0), (0, 15)
- Non-satisfying pair: (3, 1)
- y = 5x - 1
Defining Variables and Writing Equations
- Caroline's scenarios:
- Total hours worked: x + y = 40 (where x = day job hours, y = evening job hours).
- Total earnings: 15x + 11y = 540.
- Justin's earnings can be described by:
- Current job: y = 500 + 0.06x (where x is weekly sales).
- New job: y = 800 + 0.04x.
- Piggy bank contains $5.25 in nickels (n) and dimes (d): 0.05n + 0.10d = 5.25.
Graphing Relations
- Graph the equations derived from Caroline’s work hours and earnings.
- Visual representation aids in understanding constraints and possibilities in the equations.
Analyzing Job Offers
- Justin's weekly sales average around $18,000.
- The decision to accept the new job should consider total earnings compared to current position after commission.
Deb's Monthly Budget
- Deb pays 0.10perminuteforcalls,0.10 per minute for calls, 0.10perminuteforcalls,0.06 per text; total budget is $25.
- Use a table to list combinations of calls and texts within the $25 limit.
- Graphical representation of spending can show relationship between usage of calls and texts.
Leah's Earnings Evaluation
- Leah earns a fixed salary plus commission: y = 1200 + 0.035x (x is sales).
- Last month's sales totaled $96,174, yielding commissions to check against her reported pay.
- Verify if reported pay of $4,566.09 aligns with her earnings based on actual sales and commission structure.
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Description
Test your understanding of linear equations and relationships through this quiz. You'll evaluate various ordered pairs against the equation 2x + 4y = 20 and apply practical math skills to budget for muffins and doughnuts at a bake sale.
