applications of two-step equations
guided notes
essential question
how do i write and solve two - step equations from word problems?
real world problems
↓
equations
- you can write an ____ to represent two - step equations in real world situations.
- you will need to translate ____ into ____. use the list of key words below to help. it can also help to identify what the variable represents.
- after you write the equation, you can ____ it with inverse operations to answer the problem.
key words
- identify key words that can be translated into math symbols. place the following words in the correct blanks below:
division multiplication equal sign addition subtraction
- ____: the same as, equivalent, is
- ____: each, every, per, product (this will be the coefficient)
- ____: more than, increased by, total, gains, altogether, sum, ↑
- ____: less than, decreased by, difference, fewer, ↓
- ____: quotient, half, split, shared equally.
1. adam bought season passes for six flags. it cost $60 to join, plus $20 for each ticket purchase after. if he spent a total of $240, how many tickets did adam purchase?
variable: ____
equation: ____
solution: ____
2. josh collects baseball cards. he has four more than twice the number that his brother has. if josh has 48 baseball cards, then how many does his brother have?
variable: ____
equation: ____
solution: ____
3. if the perimeter of the isosceles triangle below is 22, what is the value of x?
(image of an isosceles triangle with two sides labeled x and the base labeled 6)
equation: ____
solution: ____
4. if the sum of the angles in a triangle is 180°, what is the value of x?
(image of a triangle with angles 100°, 30°, and 2x°)
equation: ____
solution: ____
5. the windchill in alaska is - 13°f and is decreasing 2 degrees each hour. if the temperature is now - 21°f, how many hours have passed?
variable: ____
equation: ____
solution: ____
6. taylor joined a meal subscription service. she paid $15 to join, and $10.50 per meal. if she has spent a total of $99, how many meals has she purchased?
variable: ____
equation: ____
solution: ____

Question

applications of two-step equations
guided notes
essential question
how do i write and solve two - step equations from word problems?
real world problems
↓
equations
- you can write an ____ to represent two - step equations in real world situations.
- you will need to translate ____ into ____. use the list of key words below to help. it can also help to identify what the variable represents.
- after you write the equation, you can ____ it with inverse operations to answer the problem.
key words
- identify key words that can be translated into math symbols. place the following words in the correct blanks below:
division  multiplication  equal sign  addition  subtraction
- ____: the same as, equivalent, is
- ____: each, every, per, product (this will be the coefficient)
- ____: more than, increased by, total, gains, altogether, sum, ↑
- ____: less than, decreased by, difference, fewer, ↓
- ____: quotient, half, split, shared equally.
1. adam bought season passes for six flags. it cost $60 to join, plus $20 for each ticket purchase after. if he spent a total of $240, how many tickets did adam purchase?
variable: ____
equation: ____
solution: ____
2. josh collects baseball cards. he has four more than twice the number that his brother has. if josh has 48 baseball cards, then how many does his brother have?
variable: ____
equation: ____
solution: ____
3. if the perimeter of the isosceles triangle below is 22, what is the value of x?
(image of an isosceles triangle with two sides labeled x and the base labeled 6)
equation: ____
solution: ____
4. if the sum of the angles in a triangle is 180°, what is the value of x?
(image of a triangle with angles 100°, 30°, and 2x°)
equation: ____
solution: ____
5. the windchill in alaska is - 13°f and is decreasing 2 degrees each hour. if the temperature is now - 21°f, how many hours have passed?
variable: ____
equation: ____
solution: ____
6. taylor joined a meal subscription service. she paid $15 to join, and $10.50 per meal. if she has spent a total of $99, how many meals has she purchased?
variable: ____
equation: ____
solution: ____

Accepted Answer

### Problem 1: Adam's Tickets
# Explanation:
## Step1: Define Variable
Let $ x $ be the number of tickets Adam purchased.
## Step2: Form Equation
The total cost is the joining fee plus the cost per ticket times the number of tickets. So, $ 60 + 20x = 240 $.
## Step3: Subtract 60 from Both Sides
$ 20x = 240 - 60 $
$ 20x = 180 $
## Step4: Divide by 20
$ x = \frac{180}{20} $
$ x = 9 $
# Answer:
Variable: $ x $ (number of tickets)
Equation: $ 60 + 20x = 240 $
Solution: $ 9 $

### Problem 2: Josh's Baseball Cards
# Explanation:
## Step1: Define Variable
Let $ x $ be the number of cards Josh's brother has.
## Step2: Form Equation
Josh has four more than twice his brother's cards: $ 2x + 4 = 48 $.
## Step3: Subtract 4 from Both Sides
$ 2x = 48 - 4 $
$ 2x = 44 $
## Step4: Divide by 2
$ x = \frac{44}{2} $
$ x = 22 $
# Answer:
Variable: $ x $ (brother's cards)
Equation: $ 2x + 4 = 48 $
Solution: $ 22 $

### Problem 3: Isosceles Triangle Perimeter
# Explanation:
## Step1: Define Perimeter Formula
Perimeter of a triangle is the sum of its sides. For an isosceles triangle with two sides $ x $ and one side $ 6 $, the perimeter is $ x + x + 6 = 22 $.
## Step2: Simplify Equation
$ 2x + 6 = 22 $
## Step3: Subtract 6 from Both Sides
$ 2x = 22 - 6 $
$ 2x = 16 $
## Step4: Divide by 2
$ x = \frac{16}{2} $
$ x = 8 $
# Answer:
Equation: $ 2x + 6 = 22 $
Solution: $ 8 $

### Problem 4: Triangle Angles
# Explanation:
## Step1: Sum of Angles in a Triangle
The sum of angles in a triangle is $ 180^\circ $. So, $ 100 + 30 + 2x = 180 $.
## Step2: Simplify Left Side
$ 130 + 2x = 180 $
## Step3: Subtract 130 from Both Sides
$ 2x = 180 - 130 $
$ 2x = 50 $
## Step4: Divide by 2
$ x = \frac{50}{2} $
$ x = 25 $
# Answer:
Equation: $ 100 + 30 + 2x = 180 $
Solution: $ 25 $

### Problem 5: Alaska Windchill
# Explanation:
## Step1: Define Variable
Let $ x $ be the number of hours passed.
## Step2: Form Equation
Initial windchill is $ -13^\circ \text{F} $, decreasing by $ 2^\circ \text{F} $ per hour, resulting in $ -21^\circ \text{F} $. So, $ -13 - 2x = -21 $.
## Step3: Add 13 to Both Sides
$ -2x = -21 + 13 $
$ -2x = -8 $
## Step4: Divide by -2
$ x = \frac{-8}{-2} $
$ x = 4 $
# Answer:
Variable: $ x $ (hours)
Equation: $ -13 - 2x = -21 $
Solution: $ 4 $

### Problem 6: Taylor's Meals
# Explanation:
## Step1: Define Variable
Let $ x $ be the number of meals Taylor purchased.
## Step2: Form Equation
Total cost is joining fee plus cost per meal times number of meals: $ 15 + 10.50x = 99 $.
## Step3: Subtract 15 from Both Sides
$ 10.50x = 99 - 15 $
$ 10.50x = 84 $
## Step4: Divide by 10.50
$ x = \frac{84}{10.50} $
$ x = 8 $
# Answer:
Variable: $ x $ (meals)
Equation: $ 15 + 10.50x = 99 $
Solution: $ 8 $

### Key Words (Filling Blanks)
- equal sign: the same as, equivalent, is
- multiplication: each, every, per, product (coefficient)
- addition: more than, increased by, total, gains, altogether, sum, ↑
- subtraction: less than, decreased by, difference, fewer, ↓
- division: quotient, half, split, shared equally

### Essential Question Fill-Ins
- You can write an **equation** to represent two - step equations in real - world situations.
- You will need to translate **words** into **math symbols**.
- After you write the equation, you can **solve** it with inverse operations to answer the problem.

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 1: Adam's Tickets

Step1: Define Variable

Step2: Form Equation

Step3: Subtract 60 from Both Sides

Step4: Divide by 20

Step1: Define Variable

Step2: Form Equation

Step3: Subtract 4 from Both Sides

Step4: Divide by 2

Step1: Define Perimeter Formula

Step2: Simplify Equation

Step3: Subtract 6 from Both Sides

Step4: Divide by 2

Answer:

Problem 2: Josh's Baseball Cards