MTH 100 CBI Applications of Linear Equations Formulas and Problem Solving

Objectives 1.Solve a Formula for a Given Variable. 2.Solve Application Problems Involving Geometric Formulas 3.Solve Application Problems Involving Money 4.Solve Application Problems Involving Mixtures

Objective 1 Solving a formula for a specific variable involves isolating that variable. All of the techniques used in solving a linear equation are valid.

Objective 1 Examples 1.Solve the formula C = tm for t. 2.Solve the formula for s.

Objective 2 The three most commonly-used formulas involve perimeter of a triangle (P = a + b + c), perimeter of a rectangle (P = 2l + 2w), and area of a triangle (A = ½ bh). In many cases, drawing a picture will help to illustrate the problem situation.

Objective 2 Examples 1.An athletic field is twice as long as it is wide. If the perimeter of the field is 78 meters, determine the dimensions of the field. 2.The area of a triangular sail for a boat is 96 square feet. If the base of the sail is 8 feet long, find its height.

Objective 3 Important: simple interest is calculated by multiplying the amount invested by the interest rate (expressed as a decimal). In many cases, a table is used to set up the equations needed to solve the problem.

Objective 3 Example Juanita has $39,000 to invest in two accounts that pay simple interest on an annual basis. One pays 6% simple interest and the other pays 5% simple interest. How much would she have to invest in each account to earn a total of $2,150 after one year?

Objective 4 Mixture problems are very similar to money problems in the way they are set up.

Objective 4 Examples 1.Suppose 2 pints of a 5% alcohol solution are mixed with 8 pints of a 90% alcohol solution. What is the concentration of alcohol in the next 10-pint mixture? 2.How much of an 80% orange juice drink must be mixed with 55 gallons of a 20% orange juice drink to obtain a mixture that is 50% orange juice?