2 3 Equations Involving Decimals and Problem Solving

2. 3 Equations Involving Decimals and Problem Solving In this section we will concentrate on solving equations containing decimals. It is often easier (but not always necessary) to clear the decimals by multiplying both sides by an appropriate power of 10. Procedure: To clear decimals in equations 1. Determine the smallest decimal place that exists in the equation i. e. tenths, hundredths, thousandths, etc. 2. Multiply both sides of the equation by an appropriate power of 10 to change all constants and coefficients to whole numbers. 10 ths --use 10, 100 ths--use 100, etc. 3. Solve the equation. Since the smallest decimal place is the 10 ths, multiply both sides of the equation by 10. Check: Then solve. Solution: Note: The procedure of “clearing the decimals” is not absolutely necessary. Dividing both sides by 1. 6 would also work. Your Turn Problem #1 Bobs. Math. Class. Com Copyright © 2010 All Rights Reserved. 1

2. 3 Equations Involving Decimals and Problem Solving Since the smallest decimal place is the 10 ths, multiply both sides of the equation by 10. Solution: Check: Alternative Solution Subtract 0. 4 x on both sides. -0. 4 x * 0. 6 x =12 0. 6 * (1 x – 0. 4 x = 0. 6 x) Then divide both sides by 0. 6. Your Turn Problem #2 Bobs. Math. Class. Com Copyright © 2010 All Rights Reserved. 2

2. 3 Equations Involving Decimals and Problem Solving Solution: Since the smallest decimal place is the 100 ths, multiply both sides of the equation by 100. Check: Your Turn Problem #3 Bobs. Math. Class. Com Copyright © 2010 All Rights Reserved. 3

2. 3 Equations Involving Decimals and Problem Solving Coin Problems The number of coins value of each coin = total value of the coins. Example: Find the value of 12 nickels, 3 dimes and 4 quarters. Solution: 12(0. 05) + 3(0. 10) + 4(0. 25) The value of the coins is $1. 90 Example 4. 0. 60 + 0. 30 + 1. 00 = 1. 90 Samantha has a collection of nickels, dimes, and quarters worth $15. 75. She has 10 more dimes than nickels and twice as many quarters as dimes. How many coins of each kind does she have? 1 st, write down the unknowns. Let x be the unknown being “referred to”. (nickels) Then translate to obtain expression for the other unknowns. # of nickels = x The equation will be the number of # of dimes = x +10 coins value of each coin = total # of quarters = 2(x + 10) value of the coins. Replace the solution to the equation into the let statements to answer the question. Your Turn Problem #4 Kerri has a collection of pennies, nickels, and dimes, worth $3. 46. The number of nickels is three less than twice the number of pennies, and the number of dimes is 5 more than # of nickels: 15 the number of nickels. How many coins of each kind does # of dimes: 15 + 10 = 25 she have? # of quarters: 2(15 + 10) = 50 Answer: Kerri has 11 pennies, 19 nickels, and 24 dimes. Bobs. Math. Class. Com Copyright © 2010 All Rights Reserved. 4

2. 3 Equations Involving Decimals and Problem Solving Example 5. Luis has 60 coins consisting of nickels, dimes, and quarters worth $4. 50. He has twice as many dimes as quarters. Find the number of each kind of coin? # of quarters = x (since quarters is being “referred to” # of dimes = 2 x (twice as mansince quarters is being “referred to” # of nickels = 60 – 3 x (total # of coins minus the sum of the # of dimes and quarters) Then, number of quarters: 5 number of dimes: 2(5) = 10 number of quarters: 60 – 3(5) = 45 Your Turn Problem #5 Kimberly has 80 coins consisting of nickels, dimes, and quarters worth $13. 50. She has three times as many dimes as nickels. Find the number of each kind of coin? Answer: Kimberly has 10 nickels, 30 dimes, and 40 quarters. The End. B. R. 12 -10 -06 Bobs. Math. Class. Com Copyright © 2010 All Rights Reserved. 5