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Add and subtract integers: word problems

Read this word problem.

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Kayla began a science experiment with

18

grams of an unknown solid. During the experiment, the change in the mass of the solid was

-7

grams. What was the mass of the solid at the end of the experiment?

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To solve the problem, Edna subtracted

18 - (-7)

and came up with an answer of

25

grams. Is Edna correct? Why or why not?

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(A)Yes, Edna is correct.

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(B)No. The answer should have been

-25

25

grams, because the mass of the solid decreased.

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(C)No. Edna should have added

18 + (-7)

because she needed to add the initial mass and the change in mass.

Read this word problem.

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The afternoon temperature in Biscoff Bay was

-2 \, ^{\circ}\mathrm{F}

. By midnight, a warm front moved in and the temperature rose to

11 \, ^{\circ}\mathrm{F}

. What was the change in temperature from afternoon to midnight?

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To solve the problem, Ross subtracted

11 - (-2)

and came up with an answer of

13 \, ^{\circ}\mathrm{F}

. Is Ross correct? Why or why not?

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(A) Yes, Ross is correct.

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(B) No. The answer should have been

9 \, ^{\circ}\mathrm{F}

13 \, ^{\circ}\mathrm{F}

, because the difference between

11

2

9

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(C) No. Ross should have added

-2 + 11

because the temperature rose.

Read this word problem.

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Amanda is playing her new video game, Track Runner. At first, she earned

20

points for winning a sprint. Then in the next race, she got

-25

points when she knocked over most of her hurdles. What is Amanda's total score now?

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To solve the problem, Amy added

20 + (-25)

and came up with an answer of

5

points. Is Amy correct? Why or why not?

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(A)Yes, Amy is correct.

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(B)No. The answer should have been

-5

5

, because Amanda lost more points than she gained.

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(C)No. Amy should have subtracted

20 - (-25)

because Amanda earned negative points.

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Read this word problem.

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In science class, Antonio started an experiment using a solution with a temperature of

-5 \, ^{\circ}\mathrm{C}

. During the experiment, the change in the solution's temperature was

-4 \, ^{\circ}\mathrm{C}

. What was the final temperature of Antonio's solution?

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To solve the problem, Antonio added

-5 + (-4)

and came up with an answer of

-9 \, ^{\circ}\mathrm{C}

. Is Antonio correct? Why or why not?

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(A) Yes, Antonio is correct.

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(B) No. The answer should have been

9 \, ^{\circ}\mathrm{C}

-9 \, ^{\circ}\mathrm{C}

, because a negative plus a negative is always a positive.

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(C) No. Antonio should have subtracted

-5 - (-4)

because the temperature dropped.

Osvoldo has a goal of getting at least

30\%

of his grams of carbohydrates each day from whole grains. Today, he ate

220

grams of carbohydrates, and

55

grams were from whole grains.

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Did Osvoldo meet his goal? Why?

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\square

\square

grams of whole grains

\square

What is the value of the expression below when

y=2

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9y^{2}+6y-5

A household aquarium tank in the shape of a rectangular prism has a base length of

24\,\text{in}

and a base width of

15\,\text{in}

. The height of the water is

12\,\text{in}

above the base. During cleaning,

900\,\text{cubic inches}

of water is removed. What is the absolute value of the change in the height of the water in inches?

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The number of students at Anna's middle school was

560

3

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Compared to the number of student

3

years ago, this year the number of boys decreased by

18 \%

and the girls increased by

10 \%

. Then, the total number of students decreased by

5 \%

. How many boys and girls are there in Anna's class this year?

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[ Hint: Note that the answer is the number of boys and girls this year.]

A bank records deposits as positive numbers and withdrawals as negative numbers. Mike withdrew

60

from his bank account

3

times. What is the change in Mike's account balance after all withdrawals?

What number must be subtracted from

67345643

54903891

An amusement park received

4800

visitors over a weekend. If

60 \%

of the visitors came on Saturday, how many visitors came on Sunday?

2 \sqrt{3}+3 \sqrt{3}

A \sqrt{B}

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A=\_\_\_\_\_

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B=\_\_\_\_\_

Ramón makes nectar for a hummingbird feeder by mixing

8

cups of water with

2

cups of sugar. Tiffany makes nectar by mixing

9

cups of water with

3

cups of sugar. Whose nectar is more sugary? Explain.

f(x)=2x+3

g(x)=x^{2}-4x

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Which of the following is equivalent to

g(f(x))

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1

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4x^{2}+4x-3

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4x^{2}-8x-3

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4x^{2}+4x+21

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2x^{2}-8x+3

During last year's basketball season, Jackson attempted

150

free throws of which he made

120

. So far this season, he's attempted

24

16

. A player's free-throw percentage is defined to be the percent of free-throws made out of the number of free-throws attempted. Assuming calculations began with the start of last year's season, which of the following best approximates Jackson's overall free-throw percentage to date?

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1

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67\%

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73\%

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78\%

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80\%

A cylindrical glass has a volume of approximately

354 \text{ cm}^3

. The glass has a diameter of

6 \text{ cm}

and is filled to

2\text{ cm}

from the top with water. A golf ball

4\text{ cm}

in diameter is placed into the glass.

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Complete the statements.

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The space remaining in the glass is ____ and the volume of the golf ball is ____.

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Therefore, putting the golf ball in the glass of water ____ cause the water to overflow.

Ms. Garcia buys a fancy coffee drink every day for

\$ 4

. She is thinking of getting regular coffee instead because it only costs

\$ 2

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Ms. Garcia works out that switching could save her

\$ 1,460

a year. Does that sound about right?

Ella bought stock in a company two years ago that was worth

x

dollars. During the first year that she owned the stock, it increased by

16 \%

. During the second year the value of the stock increased by

40 \%

. Write an expression in terms of

x

that represents the value of the stock after the two years have passed.

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Last year at a certain high school, there were

75

ninth graders on the honor roll and

90

tenth graders on the honor roll. This year, the number of ninth graders on the honor roll increased by

24 \%

and the number of tenth graders on the honor roll increased by

20 \%

. By what percentage did the total number of students on the honor roll increase? Round your answer to the nearest tenth (if necessary).

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Last year at a certain high school, there were

130

ninth graders on the honor roll and

92

tenth graders on the honor roll. This year, the number of ninth graders on the honor roll increased by

20 \%

and the number of tenth graders on the honor roll increased by

25 \%

. By what percentage did the total number of students on the honor roll increase? Round your answer to the nearest tenth (if necessary).

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Last year at a certain high school, there were

124

ninth graders on the honor roll and

120

tenth graders on the honor roll. This year, the number of ninth graders on the honor roll increased by

25 \%

and the number of tenth graders on the honor roll increased by

5 \%

. By what percentage did the total number of students on the honor roll increase? Round your answer to the nearest tenth (if necessary).

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The stock of Company A lost

\$ 2.25

throughout the day and ended at a value of

\$ 33.75

. By what percentage did the stock decline?

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Jimmy receives his first

3

video games free then pays

\$ 50

for each game after that.

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Is the amount of money he spends on video games proportional to the number of games he owns?

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1

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1

5

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You are skiing on a mountain with an altitude of

1200

meters. The angle of depression is

21^{\circ}

. You are trying to find the distance you will be sking down the mountain. Which trigonometric function will you use to solve this?

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Select the correct response.

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\cos

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\sin

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\tan

A scientist uses a submarine to study ocean life.

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85

feet below sea level.

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- After ascending for

8

62

feet below sea level.

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Find the rate of change in the submarine's elevation in feet per second. If necessary, round your answer to the nearest tenth.

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\square

\mathrm{ft} / \mathrm{s}

Isabella spends a winter day recording the temperature once every three hours for science class. At

9 \mathrm{am}

, the temperature was

-12.6^{\circ} \mathrm{F}

9 \mathrm{am}

and noon, the temperature increased by

7.7^{\circ} \mathrm{F}

. Between noon and

3 \mathrm{pm}

, the temperature rose

19.8^{\circ} \mathrm{F}

3 \mathrm{pm}

6 \mathrm{pm}

, the temperature decreased by

18.4^{\circ} \mathrm{F}

. What was the temperature at

6 \mathrm{pm}

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\square

^{\circ} \mathrm{F}

Yesterday, between noon and midnight, the temperature dropped by

30.7^{\circ} \mathrm{F}

. If the temperature was

-4.2^{\circ} \mathrm{F}

at midnight, what was it at noon?

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\square

{ }^{\circ} \mathrm{F}

Katy tried to solve an equation step by step.

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r-3=14.3

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r-3+3=14.3-3 \quad

1

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r=11.3 \quad

2

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Find Katy's mistake?

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1

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1

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2

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(C) Katy did not make a mistake

Katy tried to solve an equation step by step.

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r-3=14.3

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r-3+3=14.3-3 \quad

1

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r=11.3 \quad

2

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Find Katy's mistake?

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1

\newline

1

\newline

2

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(C) Katy did not make a mistake

At Imelda's fruit stand, you bought

5

4

\$10

, and your friend bought

5

5

\$11

. Using this information, is it possible to determine the cost of one apple and one orange from the fruit stand? If so, what do they cost? If not, why not?

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1

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(A) Yes; they should charge

\$1.00

for an apple and

\$1.25

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(B) Yes; they should charge

\$1.20

for an apple and

\$1.00

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(C) No; the system has many solutions.

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(D) No; the system has no solution.

Corey and Yin are trying to decide who will get to choose where they go for lunch. They decide to flip a coin until it lands showing heads. If the first flip shows heads, then Corey gets to choose. If heads shows on the second flip or later, then Yin gets to choose.

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Is this a fair way to decide who chooses where they go lunch? Why or why not?

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1

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(A) No, Corey is most likely to get to choose.

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(B) No, Yin is most likely to get to choose.

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(C) Yes, they both have an equal probability of choosing.

Katy tried to solve an equation.

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r-3=14.3

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r-3+3=14.3-3 \quad

\newline

r=11.3 \quad

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Where did Katy make her first mistake?