Section 2.6 Percent, Rate, and Mixture Problems 161 Troubleshooting Common Errors The most common errors in solving word problems occur in setting up the equation incorrectly. Example 5 illustrates some of these errors. �� ������������������������ ������������������ A problem and an incorrect solution are given. Provide the correct solution and an explanation of the error. 5a. A golf club is originally priced at $224.99 and is on sale for $149.99. What is the discount rate? �������������������������������������� ���������������������������������������������������������������� The discount amount is the discount rate times the original amount. So, the equation is 224.99 - 224.99x = 149.99 -224.99x = -75 -224.99x = -224.99 -75 -224.99 x ≈ 0.3333 So, the discount rate is 33.3%. inal ale 224.99 9 4.9 x iscount 5b. Jackson has $20,000 in a retirement account that he wants to invest in two different ways. He invests some of the money in a money market account that earns 5% annual interest and the other in a high risk stock fund that yields 10% annual interest. If he earned $1600 interest in a year, how much did he invest in each account? Write the equation that can be used to solve the problem. �������������������������������������� ���������������������������������������������������������������� The error is the amount remaining. If x = amount invested in the 5% account, then 20,000 - x is the amount invested in the 10% account. 0.05x + 0.10(20,000 - x) = 1600 Objective 5 ▶ Troubleshoot common errors. The original – discount = sale price. 224.99 - x = 149.99 224.99 - x - 224.99 = 149.99 - 224.99 -x = -75 x = 75 So, the discount rate is 75%. Let x = amount invested in 5% account. Then en x x - 20,000 0 = amount invested in 10%0% acco account. 0.05x + 0.10(.10 x - 20,00 20,000) = 1600 Student Check 1 a. $3000 b. $30 c. 7% d. 52.8% Student Check 2 a. $102.50 b. $6000 in the 6.5% account and $2000 in the 5% account Student Check 3 a. 21 nickels and 42 dimes b. 1.6 gal of pure antifreeze and 2.4 gal of water c. 19.44 lb of pecans and 30.56 lb of walnuts Student Check 4 a. 4 hr b. Barbara travels for 3.5 hr and Tom travels for 4.5 hr. 1. Percent applications arise in many situations. Convert percents to decimals before using them in an equation. • Discount problems: Original - discount = sale price The discount amount is a percentage of the original amount. • Markup: Original + markup = new price • Percent increase or decrease: • Recall “of ” means multiplication. 2. Simple interest is given by I = Prt. When a total amount of money is given that is split between two accounts, let x represent one amount and the remaining amount is represented as the “total amount - x.” 3. Mixture problems are set up by adding the values/ amounts from collections/solutions to equal a total value/ amount. Remember that the quantities being added must be equivalent. 4. Distance = rate × time. Organize the information in a chart by using variables for one of the columns, given amounts for another column, and then the formula to derive the third column. The expressions obtained in the last column will be used in the equation. new amount - original amount original amount ANSWERS TO STUDENT CHECKS SUMMARY OF KEY CONCEPTS
hendricks_beginning_algebra_1e_ch1_3
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