1.4 Setting Up Equations; Applications

Verbal Description Language of Math Mathematical Problem Solution Real Problem

Steps for Setting Up Applied Problem Read the problem. Assign variable(s). Make a list of known facts, translate them into mathematical expressions. If possible sketch the situation. Solve the equation for one variable, and then answer the question. Check your answer.

A total of $10,000 is invested, some in stocks and some on bonds. If the amount invested in bonds is three times the amount invested in stocks, how much is invested in each category? Let x denote the amount invested in stocks. Then 10,000 - x is the amount invested in bonds. Total amount in bonds = three times the stocks 10,000 - x = 3x

10,000 = 4x x = 2,500 The total amount invested in stocks is $2,500. The total amount invested in bonds is 10,000-2,500=7,500.

A motor boat heads upstream a distance of 50 miles on Fraser River, whose current is running at 4 miles per hour. The trip up and back takes 6 hours. Assuming that the motorboat maintained a constant speed relative to the water, what was its speed? Denote v - velocity of the boat.

Set up a table.

The total time traveled is 6 hours. We get: Solve this for v.

Solve by using a quadratic formula.

The negative answer does not make sense, so we have the velocity:

Check. So it takes 3.68 hours upstream and 2.32 hours downstream. That is a total of 6 hours.