1. Warm – up #6

Get variables on the same side & line up x, y, and z

1.

1. Warm – up #6 Solutions

-x + 2y – z = 5 x – 3y – 2z = -7-y – 3z = -2

2x + 4y + 3z =6-2x + 6y + 4z = 14

10y + 7z = 20

(-1)( ) (-1)(-2)( ) (-2)

1.

-10y – 30z = -2010y + 7z = 20-23z = 0

z = 0

(-1, 2, 0)

10y + 7(0) = 2010y = 20y = 2

x – 2(0) = 3(2) – 7x – 0 = 6 – 7x = -1

(10)( ) (10)

Homework Log

Thurs

10/22

Lesson 3 – 5

Learning Objective: To solve word problems with systems

Hw: Lesson 3 – 5 Word Problems WS

10/22/15 Lesson 3 – 5 Solving Systems with Three Variables Day 2

Algebra II

To solve word problems using systems of equations

Learning Objective

1. Find the value of two numbers if their sum is 19 and their difference is 3.

Two Variable Word Problems

x + y = 19x – y = 32x = 22x = 11

11 + y = 19y = 8

{8, 11}

2. On the first day of choir ticket sales, 12 adults and 1 student ticket sold for a total of $171. Choir took in $138 on the second day be selling 6 adult tickets and 4 student tickets. Find the price of an adult and a student ticket.

Two Variable Word Problems

12x + y = 1716x + 4y = 138

(-4) (-4) -48x - 4y =-6846x + 4y = 138-42x = -546x = 13

12(13) + y = 171156 + y = 171

y = 15

$13 for adult tix$15 for student tix

3. Jacob sold 14 banana pies and 13 strawberry pies for a total of $241. Kim sold 2 banana pies and 6 strawberry pies for a total of $80. What is the cost of each pie?

Two Variable Word Problems

14x + 13y = 2412x + 6y = 80(-7) (-7)

14x + 13y = 241-14x -42y = -560-29y = -319y = 11

2x + 6(11) = 802x + 66 = 80

2x = 14 x = 7

$7 for banana pie$11 for strawberry

4. The sum of three numbers is 6. The third number is the sum of the first and second number. The first number is one more than the third number. Find the numbers.

Three Variable Word Problems

x = 1st # y = 2nd # z = 3rd #

x + y + z = 6z = x + yx = z + 1

x + y + z = 6x + y – z = 0x - z = 1

4.

Solve by Elimination

x – 3 = 1x = 4

x + y + z = 6x + y – z = 0x - z = 1

(-1) (-1)

-x - y - z = -6x + y – z = 0-2z = -6z = 3

4 + y + 3 = 67 + y = 6y = -1

{4, -1, 3}

5. Anna is training for a triathlon. In her training routine each week, she runs 7 times as far as she swims and she bikes 3 times as far as she runs. One week, she trained a total of 232 miles. How far did she run that week?

Three Variable Word Problems

x = swim y = run z = bike

x + y + z = 232y = 7xz = 3y

x + y + z = 232-7x + y = 0 -3y + z = 0

5.

Solve by Elimination

-7x + y = 0 x + 4y = 232

x + y + z = 232-7x + y = 0 -3y + z = 0(-1) (-1)

x + y + z = 232 3y – z = 0x + 4y = 232

(-4) (-4)

28x -4 y = 0 x + 4y = 23229x = 232x = 8

5.

Solve by Eliminationy=7(8)y = 56

z = 3(56)z = 168

Swim 8 milesRun 56 milesBike 168 miles

6. Sports Chalet sold 10 gloves, 3 bats, and 2 bases for $99 on Monday. On Tuesday, it sold 4 gloves, 8 bats, and 2 bases for $78. On Wednesday, it sold 2 gloves, 3 bats, and 1 base for $33.60. What are the prices of each item?

Three Variable Word Problems

x = glove y = bat z = base

10x + 3y + 2z = 994x + 8y + 2z = 782x + 3y + z = 33.60

6.

Solve by Elimination

10x + 3y + 2z = 99-4x – 6y – 2z = -67.26x – 3y = 31.8

10x + 3y + 2z = 994x + 8y + 2z = 782x + 3y + z = 33.60

(-1) (-1)

10x + 3y + 2z = 99-4x – 8y – 2z = -786x – 5y = 21

(-2) (-2)

6.

Solve by Elimination6x – 5y = 216x – 3y = 31.8

(-1) (-1)

Glove $8Bat $5.40Base $1.40

-6x + 5y = -216x – 3y = 31.82y = 10.8y = 5.4

6x – 3(5.4) = 31.86x – 16.2 = 31.86x = 48x = 8

4(8) + 8(5.4) + 2z = 7832 + 43.2 + 2z = 7875.2 + 2z = 78 z = 1.4

7. The sum of three numbers is -4, The second number decreased by the third number is equal to the first. The sum of the first and second number is -6. What are the numbers?

Three Variable Word Problems

x = 1st # y = 2nd # z = 3rd #

x + y + z = -4y – z = xx + y = -6

x + y + z = -4-x + y – z = 0x + y = -6

7.

Solve by Elimination

x + (-2) = -6x = -4

x + y + z = -4-x + y – z = 0x + y = -6

x + y + z = -4-x + y – z = 02y = -4y = -2

-4 + (-2) + z = -4-6 + z = -4z = 2

{-4, -2, 2}

8. The difference of two number is 2. Their sum if 20. What are the numbers?

Two Variable Word Problems

x + y = 20x – y = 22x = 22x = 11

11 + y = 20y = 9

{9, 11}

LAHS scored 37 points in a football game. Six points are award for each touchdown. After each touchdown, the team can earn one point for the extra kick, or two points for a 2-point conversion. The team scored one fewer 2-point conversions than extra kicks. The team scored 10 times during the game. How many touchdowns were made?

Ticket Out the Door

Assignment:

Pg. Lesson 3 – 5 Word Problems WS