Math 7 Unit 5 Review

Marco is saving up for a new bike that costs $217.50. He already has $70 saved and plans to mow lawns to earn the remaining amount. If he can make $15 for each lawn he mows, write an equation to find L, the number of lawns Marco needs to mow to buy the bike.

​ ​ (a)   + ​ (b)   L ​ = ​ (c)  

• 70

• 15

• 217.50

• 150

• 10

• 300

• 20

• 250

Answer explanation

To find the number of lawns Marco needs to mow, subtract the amount he already has from the cost of the bike and divide by the amount he earns per lawn. The equation is 217.50 - 70 + 15L = 0. Solving for L gives the number of lawns.

During a week-long vacation, a group of friends plans to travel 280 miles each day in their road trip. To cover a total distance of at least 2,240 miles, for how many days, d, should they continue their journey?

A.) Write an inequality to represent this situation.

​ (a)   d ​ (b)   ​ (c)  

B.) After you solve the inequality, explain what the solution means.

​ (d)  

• 280

• 2240

• 260

• The trip should continue for at least 8 days.

• The trip should continue for exactly 8 days.

• The trip should continue for no more than 8 days.

Answer explanation

To cover a total distance of at least 2,240 miles, the trip should continue for at least 8 days.

Michael budgets $146 for yoga training. He buys a yoga mat for $12.85 and pays $11 per yoga class. Write an inequality to represent the number of yoga classes, y, that Michael can take and stay within his budget.

Mathematical Equivalence

ON

John is planning to donate books to a charity event. He has already donated 120 books and aims to donate a total of at least 200 books. Write an inequality to represent the number of books, b, John needs to donate to reach his goal.

Mathematical Equivalence

ON

Match each graph to the correct inequality. Some inequalities will have to be solved BEFORE you can match them to the correct number line.

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For the annual school picnic, Mr. Thompson ordered several picnic baskets for his class. Each basket costs $6.50. The total cost for the baskets was $109.50, including a $12 delivery charge. Write and solve an equation to find y, the number of picnic baskets Mr. Thompson ordered.

• y = 15

• y = 18

• y = 20

• y = 243

Solve for y in the equation 3(2y + 4) = 30.

• y = 2

• y = 3

• y = 4

• y = 5

Sam has $15.50 to spend on art supplies. He buys a set of watercolors for $5.45 at one shop. He plans to buy a sketchbook and 4 pencils at another shop. If the pencils cost $0.85 each, how much can he pay spend on the sketchbook?

$ ____

Mathematical Equivalence

ON

Samantha cycles 3 3/4 miles on Tuesday. Each day after that, she cycles the same 2 1/5 mile route every evening. Her goal is to cycle more than 10 miles by the end of the week.

Which inequality represents the least number of days after Tuesday that Samantha needs to cycle to reach her goal?

• A) 3 3/4 + 2 1/5x < 10

• B) 3 3/4 + 2 1/5x ≤ 10

• C) 3 3/4 + 2 1/5x ≥ 10

• D) 3 3/4 + 2 1/5x > 10

When solving ​ (a)   , it is important to remember that if you ​ (b)   or ​ (c)   by a negative number, you must reverse the comparison symbol.

• inequalities
• multiply
• divide
• equations
• add
• subtract