156 Chapter 2 Linear Equations and Inequalities in One Variable Student Check 2 Use the simple interest formula to solve each problem. a. Allison invested a total of $2000 in two accounts. She invested $1500 in a retirement account that pays 5.5% annual interest and the rest in a savings account that pays 4% annual interest. How much interest did she earn in 1 yr from these two accounts? b. Huynh has $8000 to invest. She invests part of the money in a money market account that pays 6.5% annual interest and the rest of the money in a CD that pays 5% annual interest. If she earns $490 interest in 1 yr, how much did she invest in each account? Mixture Problems Mixture applications involve combining two substances together to obtain a third substance. For example, combining different types of coins or dollar bills to get a monetary total or mixing two different types of liquid solutions together to make a third type of liquid solution are all mixture problems. The main point to remember when solving mixture problems is that we cannot add unlike quantities together. We must find a way to convert the different quantities to a like quantity. When working with monetary mixture problems, we convert the given number of coins or bills to its total value. We discussed this in Section 2.3 but it is worth repeating here. Coins/Bills Value of Coins/Bills To find the value of a collection of coins, multiply the number of coins by the monetary worth of the coin. 5 quarters 5(0.25) = $1.25 8 dimes 8(0.10) = $0.80 4 $10 bills 4(10) = $40 x nickels x(0.05) = $0.05x When working with liquid mixture problems, we must determine the amount of “pure” substance in each solution. To illustrate this concept, consider the percent alcohol in beer, wine, and liquor. Most law enforcement agencies consider each of the following equivalent to one drink for the purposes of calculating blood alcohol concentration. (Source: http://www.bloodalcoholcontent.org/alcoholinformation.html) Solution Amount of Alcohol 1.5 oz of 80 proof liquor (40% alcohol) 1.5(0.40) = 0.6 oz of alcohol 12 oz of regular beer (5% alcohol) 12(0.05) = 0.6 oz of alcohol 5 oz of table wine (12% alcohol) 5(0.12) = 0.6 oz of alcohol Though these three alcoholic beverages vary in quantity and percent alcohol, they each contain the same amount of alcohol. If we combine the beverages, the total amount of alcohol is the sum of the alcohol found in each beverage. This is true not only when dealing with alcoholic beverages, but for any combination of solutions with different concentrations. ������������ To find the amount of substance in a solution, multiply the given amount by the strength of the solution. Objective 3 ▶ Solve mixture applications.
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