Learning Targets
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.
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.
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.
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.