9.9 (Day 2) Systems of Linear Equations in Three Variables – Word Problems

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## 9.9 (Day 2) Systems of Linear Equations in Three Variables – Word Problems

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1. 9.9 (Day 2) Systems of Linear Equations in Three Variables – Word Problems

2. Example Alex has nickels, dimes, and quarters worth \$3.05. The number of dimes is six less than the sum of the number of nickels and quarters. If there are 24 coins in all, how many of each type of coin does Alex have? • Identify variables: n = # of nickels d = # of dimes q = # of quarters  worth 5¢ each  worth 10¢ each  worth 25¢ each

3. Example Alex has nickels, dimes, and quarters worth \$3.05. The number of dimes is six less than the sum of the number of nickels and quarters. If there are 24 coins in all, how many of each type of coin does Alex have? • Write the equations: 5n + 10d + 25q = 305 d = n + q – 6 n + d + q = 24 • rewrite in order • n – d + q = 6

4. Example • Solve: 5n + 10d + 25q = 305 n – d + q = 6 n + d + q = 24 ( )(10) 2n + 2q = 30 n + q = 15 ( )(–15) 5n + 10d + 25q = 305 10n – 10d + 10q = 60 n + 7 = 15 n = 8 15n + 35q = 365 8 + d + 7 = 24 –15n – 15q = –225 d = 9 20q = 140 8 nickels, 9 dimes, 7 quarters q = 7

5. Homework #5 Pg. 448 13, 15 Word Problems 1 – 3 all