PROBLEMS ON MODELING WITH LINEAR EQUATIONS WORD PROBLEMS

Problem 1 :

The population of Jose’s town in 1995 was 2400 and the population in 2000 was 4000. Let x represent the number of years since 1995.

Write a linear equation, in slope intercept form, that represents this data.

i) Use the equation to predict the population in Jose’s town in 2010.

Solution :

(1995, 2400) (2000, 4000)

Slope = (4000 - 2400) / (2000 - 1995)

= 1600/5

slope = 320

Linear function will be in the form, y = mx + b

Here x is the independent variable and y is the dependent variable.

y = 320x + b

At 1995, x = 0 then b = 2400

y = 320x + 2400

At 2010, x = 15 then 

y = 320(15) + 2400

= 4800 + 2400

y = 7200

Problem 2 :

Randy owns a computer store. In 1990, he sold 150 monitors. In 2000, he sold 900 monitors.

Let x represent the number of years since 1990. Write a linear equation, in slope-intercept form, that represents this data.

i) Use the equation to predict the number of monitors Randy will sell in 2007.

Solution :

At 1990, x = 0, then the number of monitors sold = 150

At 2000, x = 10, the number of monitors sold = 900

(0, 150) and (10, 900)

Rate of change = (900 - 150) / (10 - 0)

= 750 / 10

= 75

y = 75x + b

y = 75x + 150

At 2007, x = 2007 - 1990 ==> 17

Applying x = 17, we get

y = 75(17) + 150

y = 1275 + 150

y = 1425

So, number monitors sold in the year 2017 is 1425.

Problem 3 :

Romi opened a gift shop in 1995 and closed it in 2000. In 1995, her inventory of stuffed animals was 350. In 2000, her inventory of stuffed animals was 0. Let x represent the number of years since 1995.

Write an equation, in slope-intercept form, that represents that data.

i) Use the equation to estimate Romi’s inventory of stuffed animals in 1998.

Solution :

At 1995, x = 0, then the number of stuffed animals = 350

At 2000, x = 5, the number of monitors sold = 0

y = mx + b

Applying the point (0, 350), we get

350 = m(0) + b

b = 350

At 2000,  x = 5, the number of stuffed animals = 0

Applying this value, we get

0 = m(5) + 350

5m = -350

m = -70

y = -70x + 350

At 1998, x = 3, the number of stuffed animals.

y = -70 (3) + 350

y = -210 + 350

y = 140