Writing Equations

Example 1A James 2

Example 1A James 3

Example 1A James 4

Example 1A James 5

Example 1A m + 1.50 + 5.25 = 10 m + 6.75 = 10 James 6

Example 1A m + 6.75 = 10 - 6.75 - 6.75 m = 3.25 The magazine cost $3.25 James 7

Example 1B The weight limit checked baggage is 50 pounds. Lucy’s suitcase weighs 49.6 pounds, just under the limit. Her suitcase weighs 2.4 pounds, her clothes weigh 30.5 pounds, and her toiletry items are 6.2 pounds. The only items she did not weigh were her shoes. How much do these weigh?

Example 1B 2.4 + 30.5 + 6.2 + x = 49.6

Example 1B 2.4 + 30.5 + 6.2 + x = 49.6 39.1 + x = 49.6

Example 1B 2.4 + 30.5 + 6.2 + x = 49.6 39.1 + x = 49.6 -39.1 -39.1 x = 10.5

Example 1B The weight limit checked baggage is 50 pounds. Lucy’s suitcase weighs 49.6 pounds, just under the limit. Her suitcase weighs 2.4 pounds, her clothes weigh 30.5 pounds, and her toiletry items are 6.2 pounds. The only items she did not weigh were her shoes. How much do these weigh? 10.5 pounds

Example 2A Sierra walks her dog Pepper twice a day. Her evening walk is two and a half times as far as her morning walk. At the end of the week she tells her mom, “I walked Pepper for 36.75 miles this week!” How long is her morning walk? Brooke 13

Morning (w) Afternoon (2.5w) One Day Example 2A Morning (w) Afternoon (2.5w) One Day Brooke 14

Example 2A How many miles did she walk each day? 3.5w is one day One Day = how many miles? How many miles did she walk each day? Brooke 15

Example 2A A week (7days) is 36.75 miles 3.5w is one day One Day = how many miles? A week (7days) is 36.75 miles Brooke 16

Example 2A A week (7days) is 36.75 miles 36.75 divided by 7 = 5.25 3.5w is one day One Day = how many miles? A week (7days) is 36.75 miles 36.75 divided by 7 = 5.25 Brooke 17

Example 2A A week (7days) is 36.75 miles 36.75 divided by 7 = 5.25 3.5w is one day One Day = how many miles? A week (7days) is 36.75 miles 36.75 divided by 7 = 5.25 She walked 5.25 miles each day Brooke 18

3.5w is one day Sierra walked 5.25 miles each day. 3.5w = 5.25 Example 2A 3.5w is one day Sierra walked 5.25 miles each day. 3.5w = 5.25 Brooke 19

3.5w is one day Sierra walked 5.25 miles each day. 3.5w = 5.25 w = 1.5 Example 2A 3.5w is one day Sierra walked 5.25 miles each day. 3.5w = 5.25 w = 1.5 Brooke 20

Example 2A Sierra walks her dog Pepper twice a day. Her evening walk is two and a half times as far as her morning walk. At the end of the week she tells her mom, “I walked Pepper for 30.75 miles this week!” How long is her morning walk? Sierra walked 1.5 miles in the morning Brooke 21

Example 2B It takes Colin twice as long to finish his essay as it does his sister, Savannah. Together they spend four and half hours working on their essays. How long does Savannah spend working on her essay?

Example 2B Savannah = x Colin = 2x x + 2x = 4.5

Example 2B Savannah = x Colin = 2x x + 2x = 4.5 3x = 4.5

Example 2B Savannah = x Colin = 2x x + 2x = 4.5 3x = 4.5 x = 1.5

Example 2B Savannah spent 1.5 hours on her essay It takes Colin twice as long to finish his essay as it does his sister, Savannah. Together they spend four and half hours working on their essays. How long does Savannah spend working on her essay? Savannah spent 1.5 hours on her essay

Example 3A Riley reads 10 minutes more than 3 times as many minutes than Caden reads. Riley reads 25 minutes. How long does Caden read?

Example 3A Riley reads 10 minutes more than 3 times as many minutes than Caden reads. Riley reads 25 minutes. How long does Caden read? x = the minutes Caden reads 3x + 10 = 25

Example 3A Riley reads 10 minutes more than 3 times as many minutes than Caden reads. Riley reads 25 minutes. How long does Caden read? 3x + 10 = 25 x = 5 Caden reads for 5 minutes

Example 3B Jenny has 6 more dollars more than five times the amount Tim has in his wallet. Jenny has $46. How much money does Tim have?

Example 3B Jenny has 6 more dollars more than five times the amount Tim has in his wallet. Jenny has $46. How much money does Tim have? Let x be the amount Tim has in his wallet. 5x + 6 = 46

Example 3B Jenny has 6 more dollars more than five times the amount Tim has in his wallet. Jenny has $46. How much money does Tim have? Let x be the amount Tim has in his wallet. 5x + 6 = 46 x = 8 Tim has $8 in his wallet.

Example 4 Chris spent $35 at the store. He bought 2 CDs and a $5 poster. If the CDs cost the same, how much did one CD cost? Set up an equation

Example 4 Christ spent $35 at the store. He bought 2 CDs and a $5 poster. If the CDs cost the same, how much did one CD cost? x + x + 5 = 35

Example 4 Christ spent $35 at the store. He bought 2 CDs and a $5 poster. If the CDs cost the same, how much did one CD cost? 2x + 5 = 35

Example 4 Christ spent $35 at the store. He bought 2 CDs and a $5 poster. If the CDs cost the same, how much did one CD cost? 2x + 5 = 35 x = 15

Example 5 Kate spends twice as much on lunch as she does on breakfast while a work. After a five-day work week she has spent $52.50. How much does breakfast cost?

Example 5 Kate spends twice as much on lunch as she does on breakfast while a work. After a five-day work week she has spent $52.50. How much does breakfast cost? One day is x + 2x 3x

Example 5 Kate spends twice as much on lunch as she does on breakfast while a work. After a five-day work week she has spent $52.50. How much does breakfast cost? Divide 52.50 by 5 to find the cost of one day $10.50

Example 5 Kate spends twice as much on lunch as she does on breakfast while a work. After a five-day work week she has spent $52.50. How much does breakfast cost? 3x = 10.50

Example 5 Kate spends twice as much on lunch as she does on breakfast while a work. After a five-day work week she has spent $52.50. How much does breakfast cost? 3x = 10.50 x = 3.50 Breakfast is $3.50 Lunch is $7

Example 6 Colin had $20. He bought a hot chocolate for $2.95, a bag of chips for $1.55, and a puzzle book. His change was $9.50. Write an equation to find the cost of the puzzle book.

Example 6 Colin had $20. He bought a hot chocolate for $2.95, a bag of chips for $1.55, and a puzzle book. His change was $9.50. Write an equation to find the cost of the puzzle book. 2.95 + 1.55 + x + 9.50 = 20

Example 6 Colin had $20. He bought a hot chocolate for $2.95, a bag of chips for $1.55, and a puzzle book. His change was $9.50. Write an equation to find the cost of the puzzle book. 2.95 + 1.55 + x + 9.50 = 20 14 + x = 20

Example 6 Colin had $20. He bought a hot chocolate for $2.95, a bag of chips for $1.55, and a puzzle book. His change was $9.50. Write an equation to find the cost of the puzzle book. 14 + x = 20 x = 6 The puzzle book cost $6

Example 7 Savannah has three less than four times the number of medals that Caroline has. Savannah has 21 medals, how many medals does Caroline have?

Example 7 Savannah has three less than four times the number of medals that Caroline has. Savannah has 21 medals, how many medals does Caroline have? 4x – 3 = 21

Example 7 x = 6 Caroline has 6 medals Savannah has three less than four times the number of medals that Caroline has. Savannah has 21 medals, how many medals does Caroline have? 4x – 3 = 21 x = 6 Caroline has 6 medals

Example 9 Stephanie spent $5.25 of her babysitting money. She has $20.75 left. How much money did she earn babysitting.

Example 9 Stephanie spent $5.25 of her babysitting money. She has $20.75 left. Let me equal the amount she earned babysitting. Write an equation and solve m – 5.25 = 20.75

Example 9 m – 5.25 = 20.75 m = 26 Stephanie earned $26 Stephanie spent $5.25 of her babysitting money. She has $20.75 left. Let me equal the amount she earned babysitting. Write an equation and solve m – 5.25 = 20.75 m = 26 Stephanie earned $26