Start here

Use the model to solve the first problem. Then try these quick review questions from earlier lessons.

1. 1

   Same stepsFinish what the group started. Use the model above, step for step. 🔊 Listen 💡 Hint

   Try it together — then prove it:

   1. Last year the student council washed 34 cars and raised $408. This year the goal is $500. At the same price, how many cars must they wash?
   2. Divide both quantities by 34. What does 1 car raise? (408 ÷ 34 = 12, so $12 per car.)
   3. Scale $12 up to $500. Write an equation and solve it. (12n = 500, so n = 500 ÷ 12 ≈ 41.7)
   4. Why must they wash 42 cars, not 41? (41 × 12 = 492, which is less than $500. 41 cars are not enough, so round up to 42.)
   5. With 35 cars, what price per car reaches $500? (p = 500 ÷ 35 ≈ 14.29, so at least $14.29 per car.)

   Show your work
2. 2

   Quick reviewA table pairs x = 1, 2, 3 with y = 4, 8, 12. Which equation fits? 🔊 Listen 💡 Hint

   1. Ay = x + 3
   2. By = 4x
   3. Cy = x + 4
   4. Dy = x ÷ 4

   How do you know?
3. 3

   Quick reviewA bike travels 12 miles every hour. Which equation gives distance d after h hours? 🔊 Listen 💡 Hint

   1. Ad = 12h
   2. Bd = 12 + h
   3. Cd = h ÷ 12
   4. Dd = 12 − h

   How do you know?
4. 4

   Quick reviewIn the equation y = 5x, what is y when x = 6? 🔊 Listen 💡 Hint

   1. A5
   2. B11
   3. C30
   4. D56

   How do you know?

Try these on your own

Choose an answer. Then explain how you know.

1. 5

   Think it throughBakery A charges $2 per cupcake plus a $10 delivery fee, so its cost equation is c = 2n + 10, where n is the number of cupcakes. Substituting Yelina's $110 budget, which equation should she solve to find n? 🔊 Listen 💡 Hint

   1. A2n + 10 = 110
   2. B2n + 10 = 100
   3. C2n = 110 + 10
   4. Dn = 2(110) + 10

   Why is that the answer?
2. 6

   Think it throughSolving 2n + 10 = 110 for Bakery A, how many cupcakes can Yelina buy? 🔊 Listen 💡 Hint

   1. A45 cupcakes
   2. B50 cupcakes
   3. C55 cupcakes
   4. D60 cupcakes

   How do you know? Give a second reason as well.
3. 7

   Think it throughBakery B charges $2.50 per cupcake with no fee: cost = 2.5n. Solving 2.5n = 110 gives n = 44 cupcakes. Which bakery should Yelina choose to get more cupcakes within her $110 budget? 🔊 Listen 💡 Hint

   1. ABakery A, because 50 cupcakes is more than 44 cupcakes
   2. BBakery B, because 2.5 is greater than 2
   3. CBakery A, because it has a delivery fee
   4. DThey are the same, because both cost exactly $110

   Explain your thinking. What would have to change for a different choice to be right?
4. 8

   Back to the modelThe plant produces 2.5 cars per hour, and the order needs 1,000 cars. Solving 2.5h = 1,000 gives h = 400 hours. Why do you divide instead of multiply to find h? 🔊 Listen 💡 Hint

Sort it again — on paper this time

Write the letter of the group each one belongs in.

• An 8-hour shift produces 20 cars
• Washing 34 cars raised $408 last year
• 24 hours of operation produce 60 cars
• Washing 42 cars raises $504
• Producing 1,000 cars takes 400 hours
• Washing 10 cars raises $120
• One hour of operation produces 2.5 cars
• The charge last year was $12 per car

Use the words

Fill each blank with a word from the bank.

• A value of the variable that makes an equation true is a ___.
• To replace a variable with a number so you can compute is to ___.
• That amount or more — the smallest amount that still works — is ___ ___.
• To use what you already know to say what a future amount will be is to ___.

Explain the thinking

1. 9

   Find the mistakeRead the mistake. Explain what went wrong, then show the correct step. 🔊 Listen 💡 Hint

   The mistake: Adding the rate instead of multiplying — writing 2. 5 + 8 = 10.
2. 10

   Say moreYou sorted facts between the assembly line (2.5 cars/hour) and the car wash ($12/car). How did you check that 'washing 42 cars raises $504' belonged with the car wash? 🔊 Listen 💡 Hint
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: An assembly line at an automobile manufacturing plant runs in 8-hour shifts and produces 2.5 cars per hour. Next to it, an order form reads: 1,000 cars needed in 3 weeks. A table shows: 1 hour, 2.5 cars. 8 hours, 20 cars. 16 hours, 40 cars. 24 hours, 60 cars. 🔊 Listen 💡 Hint

   Show your work

Last check

These two come from Lesson 9.3. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowExplain your thinking — The plant produces 2.5 cars per hour. Using 2.5h = 1,000, how many hours does the order of 1,000 cars take? 🔊 Listen 💡 Hint

   1. A40 hours
   2. B400 hours
   3. C997.5 hours
   4. D2,500 hours

   Explain your choice.
2. 13

   From Lesson 9.3Explain your thinking — Recreation World charges $24.95 per month. Let m = number of months and c = total cost. Which equation represents the relationship? 🔊 Listen 💡 Hint

   1. Ac = 24.95m
   2. Bc = 24.95 + m
   3. Cm = 24.95c
   4. Dc = m ÷ 24.95

   How do you know?
3. 14

   From Lesson 9.3Once Diamond has both equations, how does she use them to decide which option is better? 🔊 Listen 💡 Hint

   1. AAdd the two equations together to find one combined cost
   2. BPick whichever equation has the smaller numbers written in it, without solving anything
   3. CSubstitute the same number of songs into both equations and compare the two total costs
   4. DGraph only one equation and assume the other follows the same line

   How do you know?

Check your progress

Choose the box that best describes how you feel about each skill.