Equations and Problem Solving Using Algebra to solve

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Equations and Problem Solving Using Algebra to solve Word Problems: Counting Problems and Mixture

Equations and Problem Solving Using Algebra to solve Word Problems: Counting Problems and Mixture Problems

Definition CONSECUTIVE INTEGERS Integers that differ by one. The integers 50 and 51 are

Definition CONSECUTIVE INTEGERS Integers that differ by one. The integers 50 and 51 are consecutive and so are -10 and -9 The sum of 3 consecutive integers is 147. Find the integers. Let n = the first integer Then n+1 = the second integer And n+2 = the third integer Let n = 48 Then n+1 = 49 And n+2 = 50 9/29/2020 n + n+1 + n+2 n+n+1+n+2 3 n + 3 3 n n www. numberbender. com =n 147 = 144 = 48 2

Examples • The sum of 3 consecutive integers is 72. Find the integers. Let

Examples • The sum of 3 consecutive integers is 72. Find the integers. Let n = the first integer Then n+1 = the second integer And n+2 = the third integer n + n+1 + n+2 = 3 n + 3 = 3 n = n= 9/29/2020 72 72 69 23 www. numberbender. com Let n = 23 Then n+1 = 24 And n+2 = 25 3

Examples • The sum of 3 consecutive integers is 915. Find the integers. Let

Examples • The sum of 3 consecutive integers is 915. Find the integers. Let n = the first integer Then n+1 = the second integer And n+2 = the third integer n + n+1 + n+2 = 3 n + 3 = 3 n = n= 9/29/2020 915 912 304 www. numberbender. com Let n = 304 Then n+1 = 305 And n+2 = 306 4

Mixture Problems • John has $1. 70, all in dimes and nickels. He has

Mixture Problems • John has $1. 70, all in dimes and nickels. He has a total of 22 coins. How many of each kind does he have? Step 1: Assigning variables d = dimes Step 2: Write algebraic equation d + n = 22 Step 3: Write value equation 0. 10 d + 0. 05 n = 1. 70 9/29/2020 www. numberbender. com n = nickels 5

Mixture Problems • John has $1. 70, all in dimes and nickels. He has

Mixture Problems • John has $1. 70, all in dimes and nickels. He has a total of 22 coins. How many of each kind does he have? Step 4: Solve the mixture problem (100)(0. 10 d + 0. 05 n) = 1. 70 (100) 10 d + 5 n = 170 (100) ( d + n)= 22 (100) 10 d + 10 n = 220 9/29/2020 www. numberbender. com 6

Mixture Problems • John has $1. 70, all in dimes and nickels. He has

Mixture Problems • John has $1. 70, all in dimes and nickels. He has a total of 22 coins. How many of each kind does he have? Step 4: Solve the mixture problem 10 d + 5 n -(10 d + 10 n -5 n 9/29/2020 = 170 = -220) = -50 -5 =5 Change the sign of the 2 nd equation www. numberbender. com 7

Mixture Problems • John has $1. 70, all in dimes and nickels. He has

Mixture Problems • John has $1. 70, all in dimes and nickels. He has a total of 22 coins. How many of each kind does he have? Step 4: Solve the mixture problem 10 d + 5 n = 170 10 d + 5(10) = 170 10 d + 50 = 170 -50 Substitute “n” with 10 10 d = 120 d = 12 9/29/2020 www. numberbender. com 8

Warm Up The sum of 3 consecutive integers is 60. What are the values

Warm Up The sum of 3 consecutive integers is 60. What are the values of the 3 integers? The 3 consecutive numbers are 29, 30, and 31. 9/29/2020 www. numberbender. com 9

Mixture Problem Tickets to a movie cost $5. 00 for adults and $3. 00

Mixture Problem Tickets to a movie cost $5. 00 for adults and $3. 00 for children. If tickets were bought for 50 people for a total of $196 how many adult tickets were sold and how many children tickets were sold? 1: Assigning variables a = adults 2: Write algebraic equation a + c = 50 5 a + 3 c = 196 3: Write value equation 9/29/2020 c = children www. numberbender. com 10

Mixture Problem 4: Solve the mixture problem (-5)(a + c )= 50 (-5) -5

Mixture Problem 4: Solve the mixture problem (-5)(a + c )= 50 (-5) -5 a – 5 c = -250 5 a + 3 c = 196 -2 c = -54 -2 -2 c = 27 9/29/2020 www. numberbender. com -5 a – 5 c = -250 -5 a – 5(27) = -250 -5 a – 135 = -250 +135 -5 a = -115 a = 23 11

Mixture Problem Tickets to a movie cost $4. 00 for adults and $2. 00

Mixture Problem Tickets to a movie cost $4. 00 for adults and $2. 00 for children. If tickets were bought for 80 people for a total of $230 how many adult tickets were sold and how many children tickets were sold? a = 35 9/29/2020 c = 45 www. numberbender. com 12

Homework Amy has 32 coins consisting of dimes and quarters. If Amy has a

Homework Amy has 32 coins consisting of dimes and quarters. If Amy has a total of $5 in her pocket, how many of each coin are there? dimes = 20 9/29/2020 quarters = 12 www. numberbender. com 13