1)

There are 864 small tiles and 216 big tiles. The cost of one 8-inch tile is $3.39.

2)

There are 864 small tiles and 216 big tiles. The cost of one 8-inch tile is $3.39.

3)

No, the shape will not be a square.

If your answer does not match our answer,

• did you print the sketch and label the side lengths of squares C and D?

• if you know the area of a square, can you find its side length?

• if you know the side lengths of C and D, can you figure out any other side lengths?

If any of those ideas help you, you might revise your answer.

If your answer does match ours,

• have you clearly shown and explained the work you did?

• are you confident that you could solve another problem like this successfully?

• did you make any mistakes along the way? If so, how did you find and fix them?

• are there any hints that you would give another student?

• does this problem remind you of experiences you've had?

4)

The garden's length is 14 feet and its breadth is 10 feet.

5)

The Mallerys should arrive at the beach at 7:37 a.m.

If your answer doesn't match ours, think about these things:

• What fraction of the trip took place between the two questions the kids asked?

• How much time passed between the two questions?

• What fraction of the trip remains after Liam asks his question?

If your answer does match ours,

• have you clearly shown and explained the work you did?

• did you make any mistakes along the way? If so, how did you find and fix them?

• are there any hints that you would give another student?

• did you try the extra?

6)

Lily and Mikey each have 1/3 of a box of cereal left.

Be sure that you used algebraic techniques to find your answer.

If your answer doesn't match ours,

• did you answer the question that was asked?

• did you remember that Lily ate four times as much as Mikey did each day?

• did you remember that Lily started with a full box and Mikey started with half a box?

• did you try writing variable expressions for how much cereal each child has eaten or has left in their box?

• did you remember that each child has the same amount left when the problem ends?

• did you check your arithmetic?

If your answer does match ours,

• did you use algebraic techniques to find it?

• is your explanation clear and complete? Will someone reading it fully understand what you did and why you did it?

• did you make any mistakes along the way? If so, how did you find and fix them?

• are there any hints that you would give another student?

• did you have an "Aha!" moment? :-)

7)

Lily and Mikey each have 1/3 of a box of cereal left.

Be sure that you used algebraic techniques to find your answer.

If your answer doesn't match ours,

• did you answer the question that was asked?

• did you remember that Lily ate four times as much as Mikey did each day?

• did you remember that Lily started with a full box and Mikey started with half a box?

• did you try writing variable expressions for how much cereal each child has eaten or has left in their box?

• did you remember that each child has the same amount left when the problem ends?

• did you check your arithmetic?

If your answer does match ours,

• did you use algebraic techniques to find it?

• is your explanation clear and complete? Will someone reading it fully understand what you did and why you did it?

• did you make any mistakes along the way? If so, how did you find and fix them?

• are there any hints that you would give another student?

• did you have an "Aha!" moment? :-)

8)

Question #1

The ratio of girls to boys is normally ¾, which is the same as 3x/4x. After 4 girls leave and 6 boys leave, we can represent the number of girls and the number of boys as 3x – 4 and 4x – 6, respectively. We are told that the ratio becomes 4/5 when the field trip students leave, thus we can set up the equation (3x – 4)/(4x – 6) = 4/5. Now, we cross-multiply and solve for x. 5(3x – 4) = 4(4x – 6) → 15x – 20 = 16x – 24 → 4 = x This means there are normally 3(4) = 12 girls in the class and 4(4) = 16 boys in the class, giving us a total of 12 + 16 = 28 students.

Question #2

We will first need to set up two equations using the two totals that were provided in the question. Let h = cost of a hotdog and s = cost of a soda. 4h + 3s = 17.00 2h + 1s = 7.80 By subtracting the second equation from the first, we find that 2h + 2s = 9.20. Thus, the cost of 1 hotdog and 1 soda is 9.20/2 = $4.60.

Question #3

Since all of the students selected at least one of the choices and there were 20 + 22 = 42 “best” animal choices made, 42 – 32 = 10 students must have selected both animals.

9)

If Nancy picked 30 apples per hour for 5 hours, Nancy picked 5 × 30 = 150 apples. If Tim picks apples at a rate of 25 apples per hour, we can divide 150 apples by his rate of 25 and get 150 ÷ 25 = 6 hours.

First, take Nancy and Tim’s total of 300 apples and divide that by 40 apples per bushel to get 7.5 bushels of apples that they picked. Since one gallon of cider requires one bushel of apples, 7.5 bushels would produce 7.5 gallons of cider. Knowing there are 128 ounces per gallon, Nancy and Tim can make 7.5(128) = 960 ounces of cider. Since each cup is 6 ounces, Nancy and Tim have 960/6 = 160 cups of cider to sell. At $2.00 per cup, Nancy and Tim would make 160($2.00) = $320.00. They spent $30 per bushel, so in total, $30 × 7.5 bushels = $225.00. Therefore, in profits, Nancy and Tim would make $320 - $225 = $95.

Since they are adding 1.5 gallons of water, they will have an additional 1.5 gallons of liquid to sell without any additional expenses. Thus, those (1.5 gallons)(128 oz/gal)/(6 oz per cup) = 32 extra cups are pure profit. This will result in an additional profit of 32($2.00) = $64.00.

10)

1. Answers for the first question will vary. Check your arithmetic carefully, and be especially careful when working in base 8.

2. Answers to this part will vary as well, but you will probably end up with an expression from each term of which a (b - 1) can be factored out.