Linear Inequality Word Problem

Question

Linear Inequality Word Problem:
Jeff is buying a new car but owes $3000 on his old one. Jeff can spend no more than $18,000 to pay off his old car and buy a new one.
a) Write an inequality to show how much Jeff can spend on his car.
b) Solve the inequality

Answer 1

Jeff needs to spend $3000 no matter what.  However, we don't know the amount of the car so we'll represent it with x.  Notice that the total (sum) of the two cannot exceed $18,000 or he will run out of money.

 

(a) 3000 + x ≤ 18000

 

(b) Simply subtract 3000 from both sides of the equation.

 

x ≤ 15000