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Agriculture A farmer grows tomatoes and cucumbers in the field shown. The annual cost

of growing tomatoes is \(.27 per square foot. The annual cost of growing cucumbers is \).10 per square foot. Let x represent the width (in feet) of the tomato portion of the field.

1. In terms of x, what is the area of the tomato portion? of the cucumber portion?
2. Write and simplify an expression in terms of x for the annual cost of growing both crops.
3. Find the annual cost of growing both crops if the width of the tomato portion is 350 feet
4. 
   

Crafts You make a decorative paper chain with n links by cutting a 9 inch by 12 inch sheet of construction paper into n strips.

a. Write an expression in terms of n for the width of each paper strip.

b. Suppose you want each strip to be 0.75 inch wide. Use the problem solving strategy guess, check, and revise to find the number of links your paper chain will have.

Simplify the expression.

$2.6x-7.1x$

Challenge The problem below is a variation of one that appears in the ancient Chinese text Nine Chapters on the Mathematical Art. (In the problem, a tou is a Chinese unit of measure.)

A goat, a horse, and a cow mistakenly enter a farmer’s wheat field and eat some stalks of wheat. The horse eats twice as many stalks as the goat, and the cow eats twice as many stalks as the horse. The farmer demands 5 tou of wheat from the owners of the animals to replace what was eaten. How much wheat should be replaced by the goat’s owner? by the horse’s owner? by the cow’s owner?

a. Let x be the amount of wheat (in tou) that should be replaced by the goat’s owner. What is an expression in terms of x for the amount that should be replaced by the horse’s owner? by the cow’s owner?

b. Write and solve an equation to find x. To the nearest tenth of a tou, how much wheat should be replaced by each animal’s owner?

Logical Reasoning Copy and complete the table. Use the results in each row to decide whether subtraction and division are commutative or associative operations. Explain your reasoning.

Evaluate the expression. Justify each of your steps.

$16+18+14$

Evaluate the expression. Justify each of your steps.

5. $(- 6) ( 1 ) ( 10)$

Short Response You have a canteen that holds 32 fluid ounces and weighs 0.25 pound when empty. Water weighs 0.065 pound per fluid ounce. You begin a hike with a full canteen of water. Write and simplify an expression for the weight of the canteen and water after you drink x fluid ounces. Show and justify each step of your solution.

Write a variable expression to represent the phrase.

7 more than a number

You and a friend go to the movies. You each buy a ticket for \(9.00 and a popcorn-and-drink combo for \)5.25. Describe two methods you can use to find the total amount of money you and your friend spend. What is the total amount spent?