Math 150 Applications (Word Problems)

General Strategy: 1. Understand the problem (look up any words that you don’t remember or understand 2. Visualize the problem – draw any diagrams/tables/charts if necessary; Try to estimate a reasonable range for your answer 3. Define your variables clearly – e.g. x = the first integer; w = width of the rectangle in centimeters; y = the price of the car in $; Variables usually come from the “question”. 4. Setup an equation in terms of your variables 5. Solve the equation 6. Check your answer for “reasonableness”

Solving Linear Equations (i.e. 1st degree)

Number problems: 1) The sum of 15 and a number is four times the same number. Find the number.

2) When 9 is added to 7 times a certain number, the result is equal to subtracting 3 from 10 times that number. Find the number.

3) Find three consecutive integers whose sum is 63.

Geometry Examples: 4) The perimeter of a rectangle is 24 cm. The length is twice the width. Find the dimensions. 5) A vacant lot is formed in the shape of a triangle. One side is 100ft longer than the shortest side, while the third side is 200ft longer than the shortest side. The perimeter of the lot is 1200ft. Find the lengths of the sides of the lot.

Financial Examples: 6) You paid $54 for a pair of shoes. What was the price tag of the shoes before the sales tax of 8% was added?

7) A new suit was purchased at a discount rate of 20%. With an 8.25% sales tax added, the final cost of the suit came to $151.35. What was the original price of the suit before the sales tax was added and the discount taken? 8) A company has invested $86,500 in two investments. The investments earned $6751 in interest in the first year. Part of the money was invested at a 7.4% interest rate and part was invested at 8.1%. Find the amount the company invested at each rate.

Uniform Motion D = RT 9) A truck leaves a city traveling at a speed of 72.5 km/hr and a car leaves the same city 1.25 hours later. If the car’s speed is 108 km/hr, how long will it take for the car to overtake the truck?

10) Two trains leave a city at the same time, one traveling east and the other traveling west. At the end of 9.5 hours, they are 1292 miles apart. If the rate of the train traveling east is 8 miles per hour faster than the rate of the other train, find their rates.