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Solving Word Problems That Use Linear Function
Solving Word Problems That Use Linear Function
EX 1: Suppose that a real estate office handles an apartment building with 50 units. When the rent per unit is $580 per month, all 50 units are occupied. However, when the rent is $625 per month, the average number of occupied units drops to 47. Assume that the relationship between the monthly rent x and the demand y is linear.
(a) Write a linear function that gives the demand y in terms of the rent x.
(b) Use this equation to predict the number of units occupied if the rent were $655.
f (655) = 45
(c) Predict the number of units occupied when the rent is $595.
f (595) = 49
(d) Graph the equation, and label the axes.
EX 2: Two trains leave a station at the same time traveling in opposite directions. Train A travels west and Train B travels east at a rate that is 20 mph faster than Train A. After 3 hours the two trains are 360 miles apart. How fast is each train traveling.
(a) Write a linear equation that solves this problem.
3x + 3(x + 20) = 360, where x is the speed of Train A.
(b) How fast is each train traveling?
Train A = 50 mph. and. Train B = 70 mph
EX 3: A new wireless company offers a cell phone plan that provides unlimited talk and texting for $29.95 per month, but charges $9.95 for each gigabyte allocated for data.
(a) Write a linear function that calculates the monthly bill.
f (x) = 9.95x + 29.95, where x represents the amount of data allocated.
(b) How much is the cell phone bill if you allocated 5 gigabytes of data for the month?
f (5) = $79.70
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