Math: Equations

The height of a window is 0.6 feet less than 2.5 times its width. If the height of the window is 4.9 feet, which equation can be used to determine x, the width of the window?

2.5x-0.6=4.9

Juarez scored 32 points in a basketball game. He scored twice as many baskets worth 3 points than baskets worth 2 points. How many baskets did he score worth 3 points and how many did he score worth 2 points?

8 baskets worth 3 points each and 4 baskets worth 2 points each

Sara makes and sells bracelets. She bought material for $28.50 and used it all to make 15 bracelets. Sara used the equation mc005-1.jpg to determine x, the amount she should charge for each bracelet to make a profit of $99. How much should each bracelet cost? $4.70

8.50

What is the value of x in the equation mc008-1.jpg?

256

What is the value of x in the equation 5.5x = 17.6?

3.2

Jakob buys lunch at school on Mondays, Wednesdays, and Thursdays. He spends $3.50 for each lunch. Which equation can be used to find the number of weeks, w, it will take Jakob to spend $84 on lunch?

(3-3x3.50)w=84

When solving the equation, which is the best first step to begin to simplify the equation? mc002-1.jpg

-1/2(-2)(x+3)=-10(-1/2)

What is the value of x in the equation 0.7x - 1.4 = -3.5?

-3

What is the value of x in the equation -2.4x = 8.4?

-3.5

How can mc001-1.jpg be solved for x in one step?

Add 2/3 to both sides.

Nari says, "The sum of 10 and one-third of a number is 25." She uses the bar model to write an equation to represent her statement. mc001-1.jpg Which equation can Nari write using the bar model?

25=10+1/3n

All of the items in a bicycle shop are on sale for 30% off the regular price. Rene spends $74.90 to buy a bicycle and a helmet (without taxes). If the regular price of the bicycle is $85, which equation can be used to find the regular price of the helmet, h?

0.7(85+h)=74.90

What is the value of x in the equation? mc003-1.jpg

-33

What is the value of r in the equation? mc004-1.jpg

-4

Emma buys mc018-1.jpg yards of blue fabric and some yellow fabric at a store. She buys a total of mc018-2.jpg yards of fabric. The equation mc018-3.jpg can be used to represent this situation, where y is the number of yards of yellow fabric she buys. How much yellow fabric does she buy?

1 2/3 yards

Three-fifths of the members of the Spanish club are girls. There are a total of 30 girls in the Spanish club. Which statements can be used to solve for x, the total number of members in the Spanish club? Check all that apply.

1, 4, 5

Ariel spent a total of $3.42 buying dried apricots from the bulk bins, which were on sale for $2.85 per pound. To the nearest tenth of a pound, how many pounds of dried apricots did Ariel buy?

1.2

Rona mixes 2 pounds of meat with some chopped vegetables to make a mixture. She divides the mixture into 4 equal portions. Each portion weighs 3 pounds. Which equation and solution shows the total amount of chopped vegetables she used in the mixture?

1/4(2+v)=3; v=10 pounds of chopped vegetables

Shaquille, Lyle, and Amanda collect stamps. Shaquille has one-half the number of stamps that Lyle has. Amanda has two-thirds as many stamps as Lyle. Together they have 364 stamps. How many stamps does Amanda own?

112

The Skubic family and the Shaw family went on a safari tour in which they drove their own vehicles through the park to view the animals. The cost of the tour was $5.25 per vehicle plus an additional amount for each person in the vehicle. The Skubic family had 7 people in their vehicle and paid $22.75. If the Shaw family had 3 people in their vehicle, how much did they pay?

12.75

Which equation can be used to represent the statement? Sixteen is the same as one and two-tenths times a number added to negative 8.

16=1.2n+(-8)

A 12-foot by 15-foot patio is increased by placing a stone border around the patio. The width of the border is the same all around the patio.The perimeter of the patio after it is expanded is 74 feet. mc020-1.jpg The equation which represents x, the width of the border is mc020-2.jpg. What is the width of the border?

2 1/2 ft

Which equations have the same value of x as mr024-1.jpg? Check all that apply.

2, 3, 6

A taxi driver wrote a formula to represent the mileage and fee for his last customer. He wrote the equation mr025-1.jpg, where m represents the number of miles traveled. Which statement shows the meaning of the driver's equation? Check all that apply.

2, 5

A grocer sells oranges in bags. Each empty bag weighs 2.5 ounces and each orange weighs 7.2 ounces. Khalil buys a bag of oranges that weighs 60.1 ounces. Which equation can be used to find x, the number of oranges in the bag?

2.5+7.2x=60.1

Ms. Banerjee bought a car for $22,500. The amount she paid for her new car was twice the amount she paid for her previous car, which she bought 8 years ago. Which equation shows p, the price in dollars that she paid for her previous car?

22,500=2p

Sabrina has a rug with a perimeter of 18 feet. She decides to place a border around the rug so that the new length of the rug is 8 feet and the width is 4 feet. The border is the same width all the way around. mc015-1.jpg The equation which represents x, the width of the border is mc015-2.jpg. What is the width of the border?

3/4 ft

At a big cat reserve, a male Bengal tiger weighs more than a female Bengal tiger. The male tiger weighs 445 pounds. The difference in the weights of the tigers is 97 pounds. The zookeeper created the bar diagram and equation below to find the difference in their weights. mc012-1.jpg mc012-2.jpg What is the value of f ?

348 pounds

Vance ate a salad and mc011-1.jpg of a turkey burger for dinner. The salad contained 80 calories and his entire meal contained 440 calories. Which equation can be used to determine x, the number of calories in the entire turkey burger?

440=4/5x+80

The amount Cami raised during last year's charity walk, $45.50, is mc015-1.jpg of the amount she raised this year. Which equation represents n, the number of dollars she raised this year?

45.50=0.7n

Each morning, Jon rides 1.5 miles to school and then rides to his aunt's house after school. Later in the evening, he takes the same route to get back to his house. Over 5 days, he rides 44 miles. Which equation can be used to find x, the distance from school to his aunt's house

5*(2(1.5+x))=44

Kyle is making a frame for a rectangular piece of art. The length of the frame is 3 times the width, as shown below. es025-1.jpg If Kyle uses 18 feet of wood to make the frame, what is the length of the frame? Write the answer in decimal form.

6.75

Olympia ate lunch at a restaurant. The amount of her check was $6.89. She left $8.00 on the table, which included the amount she owed plus a tip for the waiter. Which equation shows t, the amount of her tip, in dollars?

6.89+t=8.00

What is another way to write the equation mc003-1.jpg?

7(x/8)+3/4=-6

William's typical running speed is 6 km/h. The difference between his fastest speed and his typical speed is 1.5 km/h. The equation mc020-1.jpg can be used to represent this problem, where f is William's fastest speed. What is William's fastest speed?

7.5 km/h

Jalisa earned $71.25 today babysitting, which is $22.50 more than she earned babysitting yesterday. The equation mc015-1.jpg can be used to represent this situation, where d is the amount Jalisa earned babysitting yesterday. Which is an equivalent equation that can be used to find the amount Jalisa earned babysitting yesterday?

71.25*22.50=d

Kori bought 56 boxes of tiles from the home improvement store, which was es024-1.jpg of the total number of boxes that they had. How many boxes of tiles did the store have? 98

98

The first step to solve the equation mc001-1.jpg is shown below. mc001-2.jpg Which property was applied in this step?

Addition Property of Equality

Tyler wants to buy a new television that costs $312. He has already saved $96. He plans to save $24 per week over the next few weeks. Which shows the number of weeks Tyler will need to save to be able to buy the television?

B

Which bar diagram represents the equation 5x + 7.5 = 15?

C

Cedric and Insha solved the same equation using the calculations below. Cedric's Work Insha's Work mc009-1.jpg mc009-2.jpg Which statement is true about their work?

Cedric is correct because he used the inverse of subtraction and added 4.5.

Gamal spent $12.50 at the book store. The difference between the amount he spent at the video game store and the amount he spent at the book store was $17. The equation mc016-1.jpg can be used to represent this situation, where d is the amount Gamal spent at the video game store. Which equation is an equivalent equation that can be used to find the amount Gamal spent at the video game store?

NOT D

Nico, Aditi, Erick, Raj, and Sandra are solving the equation. mr023-1.jpg Each student begins to solve the problem as shown.

NTO 1, 3, 4, 5

Which method correctly solves the equation using the distributive property?

mc006-4.jpg

Zachary is solving the following equation. mc001-1.jpg Which is the best first step to begin to simplify the equation?

Distribute mc001-4.jpg over (x - 8).

A group of 4 friends went to lunch and spent a total of $40, which included the $34 food bill and the tip. They decided to split the bill and tip evenly among themselves. One of the friends used the equation mc017-1.jpg to represent the situation, where t represents the total amount of the tip. Which describes the amount each friend paid for the food and for the tip?

Each friend paid $8.50 for the food and $1.50 for the tip.

At the corner store, Nico bought 5 pencils for $0.10 each and 3 pens for $0.50 each. He used t to represent the sales tax, in dollars, that he also paid. He paid a total of $2.12, including tax. Nico wrote this equation to represent what he paid. What errors, if any, did he make? 5(0.10) + 3(0.50) - t = 2.12

He should have added t instead of subtracting t.

The first and second steps to solve the equation mc002-1.jpg are shown below. mc002-2.jpg mc002-3.jpg Which property was applied in the second step?

Multiplication Property of Equality

Which equation accurately represents this statement? Check all that apply. Negative 3 less than 4.9 times a number, x, is the same as 12.8.

NOT 1, 2

Farrah borrowed $155 from her brother. She has already paid back $15. She plans to pay back $35 each month until the debt is paid off. Which describes the number of months it will take to pay off the debt? Check all that apply.

NOT 2, 5 or 3, 6

The Schwartz family spent a total of $111.75 for Internet service for 3 months. Each

NOT A

What is the value of x in the equation mc005-1.jpg?

NOT A

In a local city, the temperature at noon is mc013-1.jpg. The temperature is expected to decrease by mc013-2.jpg each hour until the temperature reaches mc013-3.jpg. How many hours will it take for the temperature to reach mc013-4.jpg?

NOT B

Sameer choose 12 different toppings for his frozen yogurt sundae, which was mc020-1.jpg of the total number of different toppings available at the make-your-own sundae shop. To determine the number of different toppings available at the shop, Sameer set up and solved the equation as shown below. mc020-2.jpg Which best describes the error that Sameer made when solving the equation?

NOT B

Adam's car traveled 465.3 miles on 16.5 gallons of gas. Which equation can be used to determine the average number of miles that the car traveled on each gallon of gas?

NOT C

At the gym, Jasper was able to bench press 224 pounds, which was mc018-1.jpg of the weight that Balin was able to bench press. Which shows the correct equation and value of x, the weight that Balin could bench press?

NOT C

Florian ran 1.2 miles and walked 4.8 laps around the path at the park for a total distance of 3.6 miles. Which shows the correct equation and value of x, the distance of 1 lap around the path at the park?

NOT C

Which shows one way the equation can be represented in words? mc006-1.jpg

Six less than a number is the same as one and four-tenths.

What is the solution for the equation? mc002-1.jpg

a=-2

The total cost of Anja's trip to the dentist was $628.35. She paid a flat fee of $89.95 which included the checkup and cleaning and then had 4 cavities filled, each of which cost the same amount. Which shows the correct equation and value of x, the cost of each cavity filling?

mc015-1.jpg; mc015-2.jpg

What is the solution for the equation? mc003-1.jpg

n=15.1

Shawna, Dexter, and Tilana are solving the equation mc010-1.jpg. Shawna says, "I can begin by dividing each side of the equation by -2.5 to get mc010-2.jpg." Dexter says, "I can begin by distributing mc010-3.jpg to get mc010-4.jpg." Tilana says, "I can begin by multiplying each side of the equation by mc010-5.jpg to get mc010-6.jpg." Which students are correct?

only Shawna and Dexter

Malia split up the large container of salsa that she bought equally into 5 bowls to place around her house for the party. If each bowl contained 8.5 ounces of the salsa, which shows the correct equation and value of x, the total amount of salsa in the original container?

x/5=8.5 x = 42.5 ounces

What is the solution to the equation?

x=-6 1/2