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Learning Targets
- I can relate all parts of an equation like y=kx to the situation it represents.
- I can find missing information in a proportional relationship using the constant of proportionality.
Notes
Notes
Remember that if there is a proportional relationship between two quantities, their relationship can be represented by an equation of the form y=kx. Sometimes writing an equation is the easiest way to solve a problem.
For example, we know that Denali, the highest mountain peak in North America, is 20,300 feet above sea level. How many miles is that? There are 5,280 feet in 1 mile. This relationship can be represented by the equation
f = 5,280m
where f represents a distance measured in feet and m represents the same distance measured miles. Since we know Denali is 20,310 feet above sea level, we can write
20,310 = 5,280m
So m = (20,310/5,280), which is approximately 3.85 miles.
Activities
Activities
6.2 Concert Ticket Sales
6.2 Concert Ticket Sales
A performer expects to sell 5,000 tickets for an upcoming concert. They want to make a total of $311,000 in sales from these tickets.
- Assuming that all tickets have the same price, what is the price for one ticket?
- How much will they make if they sell 7,000 tickets?
- How much will they make if they sell 10,000 tickets? 50,000? 120,000? a million? x tickets?
- If they make $379,420, how many tickets have they sold?
- How many tickets will they have to sell to make $5,000,000?
6.3 Recycling
6.3 Recycling
Aluminum cans can be recycled instead of being thrown in the garbage. The weight of 10 aluminum cans is 0.16 kilograms. The aluminum in 10 cans that are recycled has a value of $0.14.
- If a family threw away 2.4 kg of aluminum in a month, how many cans did they throw away? Explain or show your reasoning.
- What would be the recycled value of those same cans? Explain or show your reasoning.
- Write an equation to represent the number of cans c given their weight w.
- Write an equation to represent the recycled value r of c cans.
- Write an equation to represent the recycled value r of w kilograms of aluminum.
Add to Your Notes
Add to Your Notes
Whether the numbers in the problem are whole numbers, large numbers, or decimals, if there is a proportional relationship between two quantities, their relationship can be represented by an equation of the form y = kx. The situations provided demonstrate the efficiency of equations for certain types of problems. Finding how many tickets should be sold in order to earn $5 million and finding the relationship between number of cans and weight and recycled value are more elegantly and efficiently handled by equations than by calculations or tables.
Summary
Summary
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