Activating Prior Knowledge – Notes

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Presentation transcript:

Activating Prior Knowledge – Notes M4:LSN 29 Word Problems Activating Prior Knowledge – Notes Graph a system that has the following solutions. One solution No solutions Infinite number of solutions Tie to LO

Learning Objective Today, we will write and solve systems of equations from word problems. CFU

Concept Development – Example #1 M4:LSN 29 Word Problems Module 4 Page 172 Concept Development – Example #1 The sum of two numbers is 361 and the difference between the two numbers is 173. What are the two numbers? Let 𝑥= the first number, Let 𝑦= the second number 𝑥+𝑦=361 Use elimination to solve the system. 𝑥−𝑦=173 267+𝑦=361 2𝑥=534 −267 −267 2 2 𝑦=94 𝑥=267 The first number is 267 and the second number is 94. CFU

Concept Development – Example #2 M4:LSN 29 Word Problems Module 4 Page 172 Concept Development – Example #2 There are 356 Grade 8 students at Euclid’s Middle School. Thirty – four more than four times the number of girls is equal to half the number of boys. How many boys are in Grade 8 at Euclid’s Middle School? How many girls? Let 𝑥= the number of boys, Let 𝑦= the number of girls 𝑥+𝑦=356 Use substitution to solve the system. Solve the second equation for 𝑥 by multiplying both sides by 2. 4𝑦+34= 1 2 𝑥 9𝑦+68=356 𝑥+32=356 2 4𝑦+34 = 1 2 𝑥 2 −68 −68 −32 −32 9𝑦=288 𝑥=324 8𝑦+68=𝑥 9 9 𝑦=32 8𝑦+68+𝑦=356 There are 324 boys and 32 girls at Euclid’s Middle School. CFU

Concept Development – Example #3 M4:LSN 29 Word Problems Module 4 Page 173 Concept Development – Example #3 A family member has some five – dollar bills and one – dollar bills in their wallet. Altogether she has 18 bills and a total of $62. How many of each bill does she have? Let 𝑥= # of $5 bills, Let 𝑦= # of $1 bills 𝑥+𝑦=18 Use elimination to solve the system by subtracting the first equation from the second. 5𝑥+𝑦=62 −𝑥−𝑦=−18 11+𝑦=18 4𝑥=44 −11 −11 𝑦=7 4 4 𝑥=11 The family member has 11 $5 bills and 7 $1 bills in their wallet. CFU

Closure – 1. What are the steps for solving a word problem using system of equations? CFU