This section summarizes the major skills taught in this chapter.Įxample 9. One solution ( a conditional equation )Ĭ.Ğvery number is a solution (an identity ) Three possible outcomes to solving an equation.Ī. Write the equation as a variable term equal to a constant.ģ.ĝivide both sides by the coefficient or multiply by the reciprocal.Ĥ. A car company charges $14.95 plus 35 cents per mile.Ģ. Generate a table to find an equation that relates two variables.Įxample 6. Study Tip: All of these informal rules should be written on note cards. Multiplication and Division (left to right)Ĥ. Order of operations: Please Excuse My Dear Aunt Sallyģ. Multiplying or dividing unlike signs: The product or quotient of two numbers with unlike signs is always negative. Multiplying or dividing like signs: The product or quotient of two numbers with like signs is always positive. Signed Numbers:Īdding or subtracting like signs: Add the two numbers and use the common sign.Īdding or subtracting unlike signs: Subtract the two numbers and use the sign of the larger, (more precisely, the sign of the number whose absolute value is largest.) If you are given information about one of the variables, you should be able to use algebra to find the other variable. You should be able to read a problem and create a table to find an equation that relates two variables. This unit introduces algebra by examining similar models. Study Tip: Remember to use descriptive letters to describe the variables. When working with percentages, remember to write them as decimals, to create tables to derive equations, and to follow the proper procedures to solve equations. Percentages play an integral role in our everyday lives, including computing discounts, calculating mortgages, savings, investments, and estimating final grades. Sale Price = Retail Price - Discount Summary: If Discount is subtracted from both sides of the equation, a formula for Sale Price is found. The retail price has two components, the sale price and the discount. The large rectangle represents the retail price. The following diagram is meant as a visualization of problem 3. (Note: the answer was rounded to the nearest cent.) The retail price for the toilet was $114.12. Solve the equation when the sale price is $97. In other words, the sale price is 85% of the retail price.Ĭ. Sale Price is the retail price minus the discount.Įxplanation: The coefficient of R is one, so the arithmetic for combining like terms is 1 - 0.15 =. Vocabulary: Retail price is the original price to the consumer or the price before the sale.ĭiscount is how much the consumer saves, usually a percentage of the retail price. The sale price of a toilet is $97 find the retail price of the toilet.Ī.Ĝomplete the table to find an equation relating the sale price to the retail price (the price before the sale). Sink Hardware store is having a 15% off sale. E is the variable that represents what Selena has to get on the final exam to get a 90 for the course.īecause Selena studied all semester, she only has to get a 79 on the final to get a 90 for the course.Įxample 3. So instead of multiplying 30% times a number, multiply 30% times E. The difference between Part a and Part b is that in Part b we don’t know Selena’s grade on the final exam. What does Selena have to get on the final exam to get a 90 for the course? Suppose Selena has an 89 homework average and a 97 test average. Pi, computes a student’s grade for the course as follows:Ī.Ĝompute Darrel's grade for the course if he has a 91 on the homework, 84 for his test average, and a 98 on the final exam.ĭarrel’s grade for the course is an 89.6, or a B+.ī. The number of questions correct is indicated by:Įxplanation: % means "per one hundred". Ethan got 80% of the questions correct on a test, and there were 55 questions. In algebra problems, percentages are usually written as decimals.Įxample 1. This section will explain how to apply algebra to percentage problems.
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