Increasing/Decreasing by a Percent - 1
Many word problems involving percents fit the above model—that is, a quantity being increased or decreased. Often you can solve these problems using one of the following formats:
Increasing/Decreasing by a Percent
Increasing/Decreasing by a Percent
As consumers, we often see quantities being increased or decreased by some percentage. For instance, a cereal box boasts ‘‘25% More.’’ An item might be on sale, saying ‘‘Reduced by 40%.’’ When increasing a quantity by a percent, first compute what the percent is, then add it to the original quantity. When decreasing a quantity by a percent, again compute the percent then subtract it from the original quantity.
Linear Applications
Linear Applications
To many algebra students, applications (word problems) seem impossible to solve. You might be surprised how easy solving many of them really is. If you follow the program in this chapter, you will find yourself becoming a pro at solving word problems. Mastering the problems in this chapter will also train you to solve applied problems in science courses and in more advanced mathematics courses.
Equations Leading to Linear Equations
Equations Leading to Linear Equations
Some equations are almost linear equations; after one or more steps these equations become linear equations. In this section, we will be converting rational expressions (one quantity divided by another quantity) into linear expressions and square root equations into linear equations. The solution(s) to these converted equations might not be the same as the solution(s) to the original equation. After certain operations, you must check the solution(s) to the converted equation in the original equation.
Formulas
Formulas
At times math students are given a formula like I = Prt and asked to solve for one of the variables; that is, to isolate that particular variable on one side of the equation. In I = Prt, the equation is solved for ‘‘I.’’ The method used above for solving for x works on these, too. Many people are confused by the presence of multiple variables. The trick is to think of the variable for which you are trying to solve as x and all of the other variables as fixed numbers. For instance, if you were asked to solve for r in I = Prt, think of how you would solve something of the same form with numbers, say,
