Lesson 2 Writing Equations to Model Relationships Part 1

Lesson 2 Writing Equations to Model Relationships Part 2

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Fill in the Blanks

Large cheese pizzas cost $5 each and large one-topping pizzas cost $6 each.

Write an equation that represents the total cost, T, of c large cheese pizzas and d large one-topping pizzas.

Put your equation in the form T= , do NOT put spaces between = and + signs.

Multiple Select

Jada plans to serve milk and healthy cookies for a book club meeting. She is preparing 12 ounces of milk and 4 cookies per person. Including herself, there are 15 people in the club. A package of cookies contains 24 cookies and costs $4.50.

A 1-gallon jug of milk contains 128 ounces and costs $3. Let n represent number of people in the club, m represent the ounces of milk, c represent the number of cookies, and b represent Jada's budget in dollars.

Select all of the equations that could represent the quantities and constraints in this situation.

• $m=12\left(15\right)$

• $3m+4c=b$

• $4n=c$

• $4\left(4.50\right)=c$

• $b=2\left(3\right)+3\left(4.50\right)$

Multiple Choice

A student on the track team runs 45 minutes each day as a part of her training. She begins her workout by running at a constant rate of 8 miles per hour for a minutes, then slows to a constant rate of 7.5 miles per hour for b minutes.

Which equation describes the relationship between the distance she runs in miles, D, and her running speed, in miles per hour?

• $a+b=45$

• $8a+7.5b=D$

• $8\left(\frac{a}{60}\right)+7.5\left(\frac{b}{60}\right)=D$

• 8(45-b)+7.5b=D

Multiple Choice

Elena bikes 20 minutes each day for exercise.

Write an equation to describe the relationship between her distance in miles, D, and her biking speed, in miles per hour, when she bikes:

at a constant speed of 13 miles per hour for the entire 20 minutes (Hint what fraction of an hour is 20mins)

• $D=13\cdot\frac{1}{3}$

• $D=13\cdot20$

• $D=13\cdot\frac{1}{20}$

• $D=13\cdot\frac{1}{4}$

Multiple Choice

Elena bikes 20 minutes each day for exercise.

Write an equation to describe the relationship between her distance in miles, D, and her biking speed, in miles per hour, when she bikes:

at a constant speed of 15 miles per hour for the first 5 minutes, then at 12 miles per hour for the last 15 minutes (Hint what fraction of an hour is 5 mins and 15 mins?)

•  $D=15\cdot\frac{1}{12}+13\cdot\frac{1}{4}$ 

•  $D=13\cdot\frac{1}{12}\cdot\frac{1}{20}$ 

• $D=13\cdot\frac{1}{20}$

•  $D=15\cdot\frac{1}{12}$ 

Multiple Choice

Joe earns $25 per yard he mows in the summer.  If he also makes a one time amount of $100 for babysitting his brother, write an equation that can be used to determine the number of yards (y) he will need to mow to go to Italy for $3,100.  

• 25y - 100 = 3,100
• 3,100 - 100 = 25y
• 25y + 100 = 3,100
• 100y + 25 = 3,100

Multiple Choice

Pizzazz Publications is having some books printed. The printer charges $800 plus $5 per book. What equation could help me find how many books can be printed for $4,000?

• 800 + 5x = 4000
• 800x + 5 = 4000
• 4000 + 5x= 800
• 800 + 5 = 4000

Multiple Choice

Ms. Jacobs is a photographer .  For each job she charges $135 for the first hour she works and $100 for each additional hour.  Ms. Jacobs charged $535 for a job she completed.  Write an equation that can be used to determine the number of hours (h) she spent on the job.

• 135x + 100 = 535
• 100x - 135 = 535
• 100x + 135 = 535
• 135x - 100 = 535

Multiple Choice

Natalie is a softball coach. She has a pitching private lesson with Kasey. Kasey's mom pays Natalie $11 per hour plus a $6 tip. Write an equation that represents the number of hours (h) of lessons Kasey took if the total cost was $39.

• 11 + 6h = 39
• 11h - 6 = 39
• 11h + 6 = 39
• 66h = 39

Multiple Choice

Penelope is going to the carnival to ride the rides. It costs $20 to get into the carnival and ride tickets are $0.50 each. Write an equation that represents the number of tickets (t) that can be purchased if Penelope plans to spend $35.

• .50t + 20 = 35
• .50t = 35
• .50 + 20t = 35 
• .50t +35 = 20