Linear Modeling and Logic Unit
4.4 Linear Modeling
Scenario 1
You buy a $200 printer and the ink cartridges cost $25 each. Write an equation for total cost.
y = 25x + 200
If your office budgets $30 per month for printer costs, how many ink cartridges can they buy the year they purchase the printer?
25x + 200 = 360
25x = 160
x = 6.4
The office can buy 6 cartridges for the year.
Scenario 2
You get a $50 Starbucks gift card for your birthday. A short latte costs $4.25.
Write an equation for how much is left on your gift card.
\(y=-4.25x+50\), where x is the number of lattes you buy.
How many short lattes can you buy with your gift card?
50 - 3.35x = 0
-3.35x = -50
x = 14.93
You can buy 14 lattes with a $50 gift card.
Scenario 3
It’s summer and Jill is filling her above ground pool. It takes 25 minutes to raise the water level 4 inches. The water level is already 10 inches. What is the rate Jill is filling the pool in inches per minute?
\( \begin{equation} \frac{4 \text{ inches}}{25 \text{ minutes}} = 0.16 \text{ inches per minute} \end{equation} \)
Write an equation for the depth of the water in the pool depending on time.
\( \begin{equation}y = 10 + 0.16x \text{ or } y = 10 + \frac{4}{25} x \end{equation} \)
If the pool is 4 feet deep, how much longer will it take Jill to fill the pool?
48 = 10 + 0.16x
38 = 0.16x
x = 237.5
It will take 237.5 minutes to fill the pool.
Scenario 4
The gas tank in your car holds 12 gallons. The dashboard statistics tells you that you get 28 miles per gallon. Write an equation for the amount of gasoline left in your tank depending on how many miles you’ve driven.
\( \begin{equation} y = 12 - \frac{1}{28} x \end{equation} \)
Your trip meter says you’ve gone 290 miles so far on this tank of gas. Can you make it to work and back (25 miles each way) without stopping for gas?
It is a 50 mile round trip.
You have 1.6 gallons left in your tank.
28 * 1.6 = 46 miles
You will not make it to work and back without putting more gas in the tank.