Name (s) Class Date MULTI-STEP EQUATIONSmissmezinesclassroom.weebly.com/uploads/5/.../multi_step_equatio… · MULTI-STEP EQUATIONS READ & UNDERSTAND (Highlight or circle important

Name (s) __________________________________ Class__________ Date_________________________

©Exceeding the CORE Question # 0

PROBLEM SOLVING

GRAPHIC ORGANIZER

MULTI-STEP

EQUATIONS

Equations with Variables on Each Side

Equations with Rational Numbers

Multi-Step Equations

Name (s) __________________________________ Class__________ Date_________________________


MULTI-STEP EQUATIONS

READ & UNDERSTAND (Highlight or circle

important keywords.)

The table shows ticket prices for an amusement park for members and non-members. For how many tickets is the cost same for members and non-members?

Ticket Prices

Members Non-

Members

Membership Fee $30 None

Ticket Price $3 $6

What do we know? (List the important facts

needed for this problem to be solved.) _________________________________________________________________________________________________________ ___________________________________ What do we want to find out? (Explain in

your own words.) _________________________________________________________________________________________________________ ___________________________________

SOLVE (Answer the problem. Show all work.)

EXPLAIN (State your answer. Give details. Explain what you did and justify your steps.)

________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________

Name (s) __________________________________ Class__________ Date_________________________





The table shows the number of T-shirts student council members sold. The total raised was $353. Write and solve an equation to find the price of one T-shirts.



your own words.) _________________________________________________________________________________________________________ ___________________________________


EXPLAIN (State your answer. Give details. Explain what you did and justify your steps.) ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________ ________________________________________________________________________

Name Number of

T-shirts sold

Pedro 10

Allison 13

Lorna 9

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Get Fit Gym charges a yearly fee of $250 plus $10 for each session with a personal trainer. Tight N’ Toned Gym charges a one time fee of $50 plus $30 per session for a personal trainer. For how many sessions is the cost of the two plans the same?



your own words.) _________________________________________________________________________________________________________ ___________________________________



Name (s) __________________________________ Class__________ Date_________________________





Mr. Grouper has budgeted $2000 for a graduation party for his son. The cost to rent the venue is $150. How much can Mr. Grouper spends per guest on food if each of the 225 guests receives a $3.50 gift?



your own words.) _________________________________________________________________________________________________________ ___________________________________



Name (s) __________________________________ Class__________ Date_________________________





Pristine House Cleaners charges $19.85 plus $32 a room. Sparkle House Cleaners charges $61.85 plus $18 a room. Write and solve an equation to find the number of rooms for which the total cost of both house cleaners is the same?



your own words.) _________________________________________________________________________________________________________ ___________________________________



Name (s) __________________________________ Class__________ Date_________________________





At the carnival, Marsha bought 10 ride tickets and 3 snacks. Each ride ticket costs $1.50 less than a snack. Marsha spent a total of $24.00. Write and solve an equation to find the cost of each snack?



your own words.) _________________________________________________________________________________________________________ ___________________________________



Name (s) __________________________________ Class__________ Date_________________________





Greg is saving to buy a tablet that costs $235. He already has $25. Each week, Greg earns $15 babysitting and $25 as a casher, but he spends $10 on lunches. Write and solve an equation to find in how many weeks Greg will have enough money saved.



your own words.) _________________________________________________________________________________________________________ ___________________________________



Name (s) __________________________________ Class__________ Date_________________________





Shirley has two different garden plots She wants to fence in each garden plot with the same number of small rocks. Write and solve an equation to find the value of 𝒙 so that the gardens plots have the same perimeter.



your own words.) _________________________________________________________________________________________________________ ___________________________________



Name (s) __________________________________ Class__________ Date_________________________





The Williams family spent a total of $26.75 at the Snack Shack. They bought 3 sandwiches and 5 beverages. Each beverage costs $2.50 less than a sandwich. Write and solve an equation to find the cost of each sandwich?



your own words.) _________________________________________________________________________________________________________ ___________________________________



Name (s) __________________________________ Class__________ Date_________________________





Ms. Campbell is hosting a toy drive for charity. Justin collected 10 more toys than Brianna. Hannah collected twice as many as Justin. If they collected 130 toys altogether, how many toys did Justin collect?



your own words.) _________________________________________________________________________________________________________ ___________________________________



Name (s) __________________________________ Class__________ Date_________________________


MULTI-STEP EQUATIONS PROBLEM SOLVING Answer Key Answer Sample Work

1. The cost is the same for 10 tickets for

members and non-members.

30 + 3𝑥 = 6𝑥 30 = 3𝑥; 10 = 𝑥

2. Each T-shirt cost $11. 10𝑛 + 13𝑛 + 9𝑛 = 353 32𝑛 = 353; 𝑛 = 11

3. The cost is the same for10 personal

training sessions.

250 + 10𝑠 = 50 + 30𝑠 250 = 50 + 20𝑠 200 = 20𝑠; 10 = 𝑠

4. Mr. Grouper can spend $4.72 per guest on food.

2000 = 150 + 225(𝑥 + 3.50) 2000 = 150 + 225𝑥 + 787.50 2000 = 225𝑥 + 937.5 1062.50 = 225𝑥; 4.72 = 𝑥

5. The total cost of both houses cleaners are the same for 3 houses

19.85 + 32𝑥 = 61.85 + 18𝑥 32𝑥 = 42 + 18𝑥 14𝑥 = 42 ; 𝑥 = 3

6. Each snack cost $3.

10(𝑠 – 1.5) + 3𝑠 = 24 10𝑠 – 15 + 3𝑠 = 24 13𝑠 – 15 = 24 13𝑠 = 39

7. Greg will have enough money seved in 7 weeks.

25 + (15 + 25)𝑤 − 10𝑤 = 235 25 + 40𝑤 − 10𝑤 = 235 25 + 30𝑤 = 235 30𝑤 = 210 𝑤 = 7

8. The value of x must be 5 in order for the

plots to have the same perimeter.

4(𝑥 + 6) = 𝑥 + 6 + 3𝑥 + 3 + 5𝑥 4𝑥 + 24 = 9𝑥 + 9 24 = 5𝑥 + 9 15 = 5𝑥 5 = 𝑥

9. Each sandwich cost $4.91. 3𝑠 + 5(𝑠 − 2.50) = 26.75 3𝑠 + 5𝑠 − 12.50 = 26.75 8𝑠 − 12.50 = 26.75 8𝑠 = 39.25 𝑠 = 4.91

10. Justin collected 35 toys.

𝑥=toys Brianna collected 10 + 𝑥=toys Justin collected 2(10 + 𝑥) =toys Hannah collected 𝑥 + 10 + 𝑥 + 2(10 + 𝑥) = 130 𝑥 + 10 + 𝑥 + 20 + 2𝑥 = 130 4𝑥 + 30 = 130 ; 4𝑥 = 100; 𝑥 = 25 10 + 𝑥 = 10 + 25 = 35

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