Multi-Step Equations
4x + 2x + 18 = 36
x = 3
10 + 3x + 7x = 30
x = 2
A certain country requires people to pass a language test and a citizenship test before they can become citizens. This year, 60% of the applicants passed the language test and 90% of those who passed the language test then passed the citizenship test. If there were 500 applicants this year, how many were granted citizenship?
Hint: Set up Proportion
x = 30 applicants passed
Solve: m/5 = 4
m = 20
Solve: 3p + 12 = 42
A video game costs v dollars, and a controller is 10 dollars cheaper. You buy 2 video games and one controller, and pay 70 dollars. How much does a video game cost?
Equation: 2v + v - 10 = 70
To Solve:
1. Combine the v terms to get 3v
2. Add by 10 on both sides (inverse operation)
3. Divide both sides by 2 to get v by itself
Final answer: $40
You have $85 in your bank account. Each week you plan to deposit $8 from your allowance and $15 from your paycheck. How many weeks from now will you have $175 in your bank account?
Equation: 8x + 15x + 85 = 175
x = 3.9 weeks so about 4 weeks
Shawn makes $97.50 after working at McDonalds for 6 hours. How many hours did he work if he made $2,700?
Hint: Set up proportion and solve!
x = 166 hours
A movie ticket costs $8. David bought 6 tickets. How much did he spend?
David spent $48
Quinton started his own tutoring business. Each month, he makes $120 from tutoring. However, he had to pay $75 in startup costs.
Hint: 12 months = 1 year
Hint: If he has to pay for costs, are we subtracting or adding?
Write and solve an equation for the amount of money, m Quinton has after 1 year
120x - 75 = m
x = 12 so plug in 12 for x
120(12) - 75 = $1365
Three friends go bowling. The cost per person per game is $5.30. The cost to rent shoes is $2.50 per person. Their total cost is $55.20. How many games did they play?
Equation: $5.30x + 3($2.50) = $55.20
$5.30x + 7.5 = $55.20
x = 9 games
Noble orders laptops for its students. Each laptop costs $900. They add a software package costing $100 per laptop. There is a one-time shipping fee of $50 for the entire order. The total bill comes to $9,050. How many laptops did Noble order?
Equation: 900x + 100x + 50 = $9050
x = 9 laptops
Josiah earns $195 in 12 hours.
Find the Unit Rate:
Hint: Unit Rate * # of hours
At this rate, how much will you earn in 40 hours?
At this rate, how much will you earn in 100 hours?
Josiah's Unit Rate is $16.25 per hour
In 40 hours: 16.25 * 40 = $650
In 100 hours: 16.25 * 100 = $1625
Amira bought 5 packs of markers. Each pack cost the same. She spent $20 total. How much did each pack cost?
Each pack costs $4
The cost to rent a construction crane is $750 per day plus $250 per hour of use. What is the maximum number of hours the crane can be used each day if the rental cost has to be $2500 per day?
Write an equation to represent this scenario.
What is the maximum number of hours the crane can be used?
Equation: $750 + $250x = $2500
Solve: x = 7 hours
Martha takes her niece and nephew to a concert. She buys T-shirts and bumper stickers for them. The bumper stickers cost $1 each. Martha’s niece wants 1 shirt and 4 bumper stickers and her nephew wants 2 shirts, but no bumper stickers. If Martha’s total is $67, what is the cost of 1 shirt?
Hint: They already tell you the cost of a bumper sticker!
Equation: 1s + 2s + 4(1) = 67
s = $21
One shirt cost $21
You and a group of your friends buy concert tickets online. Each ticket costs $50. All of you also purchase a merchandise package with each ticket for $15. The website charges a flat service fee of $10 for the entire order. You all pay a total of $335. How many tickets did you buy?
Equation: 50x + 15x + 10 = 335
x = 5 tickets
Angel practices swimming for half an hour. For the first 15 minutes, he swims at 2 mph. For the next 10 minutes, he swims at 3 mph. For the last 5 minutes, he swims at 1 mph. Approximately how far did he swim in miles?
First Step: Convert minutes to hours first!
Second Step: Find the distance (how far he swam) for each part
Third Step: Find the TOTAL distance he swam altogether.
Total distance: 0.5 miles + 0.51 miles + 0.08 miles = 1.09 miles
Answer: 1.09 miles
Marcus has a certain number of pencils. After giving away 10 pencils to his friends, he still has 10 left. How many pencils did Marcus start with?
Marcus started with 20 pencils
Caleb won 50 stickers playing basketball at his school's game night. Later, he gave two to each of his friends. He only has 10 remaining. How many friends did he give stickers to?
1. Write an equation to represent, f the number of friends Caleb gave stickers to.
2. Solve the equation
Equation: 50 - 2f = 10
Solve: f = 20 friends
A family buys airline tickets online. Each ticket costs $167. The family buys travel insurance with each ticket that costs $19 per ticket. The website charges a fee of $16 for the entire purchase. The family is charged a total of $1132. How many tickets did the family buy?
Equation: $167x + $19x + $16 = $1132
x = 6 tickets
The perimeter of a table is the sum of all of its sides. A table is measured to be 1a+1b inches long and 5b+12 inches wide.
Hint: Perimeter = 4 sides
Answer: 2a + 12b + 24
To travel between Pembroke and Quinnville, a person can choose one of two routes. Joe chose the route that was a total of 150 miles and drove an average of 40 miles per hour. Frank chose the route that was a total of 200 miles. For the first 3 hours of his trip, Frank drove at an average of 60 miles per hour. However, during the last 20 miles of his trip Frank encountered construction and drove an average of 20 miles per hour. If both Frank and Joe departed Pembroke at the same time, who arrived first at Quinnville and by how many minutes?
Hint: To find Joe's time, find the unit rate!
Hint: To find Frank's time, find the unit rate for the last 20 miles and add to that the hours he already travelled (3 hours)
Joe arrives faster than Frank
Joe: 3.75 hours
Frank: 4 hours
Last week Julia ran 25 miles more than Colette. Julia ran 90 miles. How many miles did Colette run?
1. Write an equation to represent, m the number of miles Colette ran.
2. Solve the equation.
Equation: m + 25 = 90
Solve: m = 65 miles
Nick is using the equation y=1700+850m to track his savings over time. He has some money saved already and puts part of his monthly paycheck into the account.
If Nick plans to use the money in the account to buy a new car that costs $16,000, how many months will he need to save?
Equation: 1700 + 850m = $16000
Solve: m = 16.8 so about 17 months