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You did these with your group. Now do them on your own — the model above is yours to copy.

1. 1

   Same stepsFinish what the group started. Use the model above, step for step.

   Try it together — then prove it: Last year the council washed 34 cars and raised $408. What did they charge per car? Divide: 408 ÷ 34 = $12. At $12 per car, let n = cars washed and t = total raised: t = 12n. The goal is $500, so 12n = 500 means n = 500 ÷ 12, which is about 41.7 — so they must wash at least 42 cars, because 41 cars raise only 41 × 12 = $492. Or fix the cars instead: if they predict 35 cars, then 35p = 500 gives p = 500 ÷ 35, about $14.29 — so they must charge at least $14.30 per car. Now prove it: say why that move had to work at all — not just that it did.

   Show your work
2. 2

   Warm restartA table pairs x = 1, 2, 3 with y = 4, 8, 12. Which equation fits?

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

   How do you know?
3. 3

   Warm restartA bike travels 12 miles every hour. Which equation gives distance d after h hours?

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

   How do you know?
4. 4

   Warm restartIn the equation y = 5x, what is y when x = 6?

   1. A30
   2. B11
   3. C5
   4. D56

   How do you know?

You answered these out loud. Now write them.

Answer, then say how you know — the reason is the part that counts.

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?

   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?

   1. A50 cupcakes
   2. B55 cupcakes
   3. C60 cupcakes
   4. D45 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?

   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?

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 mistakeAnother student made this exact mistake in this lesson. Explain why it is wrong, then write what they should have done.

   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?
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.

   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?

   1. A400 hours
   2. B2,500 hours
   3. C997.5 hours
   4. D40 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?

   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?

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

   How do you know?

Be honest — this tells your teacher what to do next