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Add and subtract integers: word problems

Eliana tried to solve 3.2+2(2.4−2t)=−16+t3.2 + 2(2.4 - 2t) = -16 + t. Here is her work:\newline3.2+4.8−4t=−16+t3.2 + 4.8 - 4t = -16 + t {Step 11}\newline8−4t=−16+t8 - 4t = -16 + t {Step 22}\newline8−3t=−168 - 3t = -16 {Step 33}\newline−3t=−24-3t = -24 {Step 44}\newlinet=8t = 8 {Step 55}\newlineDid Eliana solve the equation correctly?\newline(A)Yes, Eliana solved the equation correctly.\newline(B)No, Eliana made a mistake in step 11. She didn't apply the distributive property correctly.\newline(C)No, Eliana made a mistake in step 33. She didn't apply the subtraction property of equality correctly.\newline(D)No, Eliana made a mistake in step 44. She didn't apply the division property of equality correctly.
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A magician sold out 33 performances: 11 performance at a 498498-seat theater and 22 performances at a 4,0084,008-seat theater.\newlineShe estimates that is around 4,5004,500 seats in total. Is that a good estimate?\newlineChoices:\newline(A)Yes.\newline(B)No, it is much too high.\newline(C)No, it is much too low.
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Tisha tried to evaluate an expression. Here is her work:\newline490÷72×9−2×3490 \div 7^2 \times 9 - 2 \times 3\newline490÷49×9−2×3490 \div 49 \times 9 - 2 \times 3 {Step 11}\newline10×9−2×310 \times 9 - 2 \times 3 {Step 22}\newline90−2×390 - 2 \times 3 {Step 33}\newline88×388 \times 3 {Step 44}\newline264264 {Step 55}\newlineIs Tisha's work correct?\newline(A)No, Tisha made a mistake going from Step 11 to Step 22. Tisha should have multiplied 4949 and 99 before dividing. The order of operations says to multiply before you divide.\newline(B)No, Tisha made a mistake going from Step 33 to Step 44. Tisha should have multiplied 22 and 33 before subtracting. The order of operations says to multiply before you subtract.\newline(C)Yes, Tisha's work is correct.
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Valeria tried to evaluate an expression. Here is her work:\newline\newline 8+12÷4×428 + 12 \div 4 \times 4^2\newline 8+12÷4×168 + 12 \div 4 \times 16 {Step 11}\newline 20÷4×1620 \div 4 \times 16 {Step 22}\newline 5×165 \times 16 {Step 33}\newline 8080 {Step 44}\newline\newlineIs Valeria's work correct?\newline\newlineChoices:\newline(A)No, Valeria made a mistake going from the given expression to Step 11. Valeria should have multiplied 44 by 44 instead of evaluating the exponent. The order of operations says to multiply before you evaluate exponents.\newline(B)No, Valeria made a mistake going from Step 11 to Step 22. Valeria should have divided 1212 by 44 before adding. The order of operations says to divide before you add.\newline(C)Yes, Valeria's work is correct.\newline
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Read this word problem.\newlineThe overnight low temperature in Cassidy City was −17 ∘F-17 \, ^{\circ}\mathrm{F}. The overnight low temperature in Shakerville was −6 ∘F-6 \, ^{\circ}\mathrm{F}. How much warmer was Shakerville than Cassidy City?\newlineTo solve the problem, Manny subtracted −6−(−17)-6 - (-17) and came up with an answer of −11 ∘F-11 \, ^{\circ}\mathrm{F}. Is Manny correct? Why or why not?\newlineChoices:\newline(A) Yes, Manny is correct.\newline(B) No. The answer should have been 11 ∘F11 \, ^{\circ}\mathrm{F}, not −11 ∘F-11 \, ^{\circ}\mathrm{F}, because Shakerville was warmer.\newline(C) No. Manny should have added −17+−6-17 + -6 because Shakerville was warmer.
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Read this word problem.\newlineOvernight, the temperature in Mayville was −4 ∘F-4 \, ^{\circ}\mathrm{F}. But by the following afternoon, the temperature had risen 11 ∘F11 \, ^{\circ}\mathrm{F}. What was the temperature in Mayville that afternoon?\newlineTo solve the problem, Rose added −4+11-4 + 11 and came up with an answer of 7 ∘F7 \, ^{\circ}\mathrm{F}. Is Rose correct? Why or why not?\newlineChoices:\newline(A) Yes, Rose is correct.\newline(B) No. The answer should have been −7 ∘F-7 \, ^{\circ}\mathrm{F}, not 7 ∘F7 \, ^{\circ}\mathrm{F}, because a negative plus a positive is always a negative.\newline(C) No. The answer should have been 15 ∘F15 \, ^{\circ}\mathrm{F}, because the sum of the absolute values of −4-4 and 1111 is 1515.
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Read this word problem.\newlineOn a cold February morning, Colton checked the temperature on his phone and saw that it was −3 ∘C-3 \, ^{\circ}\mathrm{C}. When he checked again after school, the temperature had dropped 3 ∘C3 \, ^{\circ}\mathrm{C}. What was the temperature after school?\newlineTo solve the problem, Ellen subtracted −3−(−3)-3 - (-3) and came up with an answer of 0 ∘C0 \, ^{\circ}\mathrm{C}. Is Ellen correct? Why or why not?\newline\newlineChoices:\newline(A) Yes, Ellen is correct.\newline(B) No. Ellen should have added −3+3-3 + 3 because she needed to add the starting temperature and the change in temperature.\newline(C) No. Ellen should have subtracted −3−3-3 - 3 because the temperature started at −3 ∘C-3 \, ^{\circ}\mathrm{C} and dropped 3 ∘C3 \, ^{\circ}\mathrm{C}.
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Read this word problem.\newlineIn the morning, the temperature in Westfield City was −2 ∘F-2 \, ^{\circ}\mathrm{F}. By afternoon, a north wind caused the temperature to drop another 8 ∘F8 \, ^{\circ}\mathrm{F}. What was the afternoon temperature in Westfield City?\newlineTo solve the problem, Martin subtracted −2−(−8)-2 - (-8) and came up with an answer of 6 ∘F6 \, ^{\circ}\mathrm{F}. Is Martin correct? Why or why not?\newlineChoices:\newline(A) Yes, Martin is correct.\newline(B) No. The answer should have been −6 ∘F-6 \, ^{\circ}\mathrm{F}, not 6 ∘F6 \, ^{\circ}\mathrm{F}, because the temperature dropped.\newline(C) No. Martin should have subtracted −2−8-2 - 8 because the temperature started at −2 ∘F-2 \, ^{\circ}\mathrm{F} and dropped by 8 ∘F8 \, ^{\circ}\mathrm{F}.
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Read this word problem.\newline\newlineCamilla was swimming along the bottom of her backyard pool at a depth of 66 feet. Then, she pushed off the bottom and rose 44 feet. What is Camilla's position now relative to the surface of the pool?\newlineTo solve the problem, Jordan added −6+4-6 + 4 and came up with an answer of 22 feet. Is Jordan correct? Why or why not?\newline\newlineChoices:\newline(A)Yes, Jordan is correct.\newline(B)No. The answer should have been −2-2 feet, not 22 feet. She is underwater, so her position relative to the surface of the pool is negative.\newline(C)No. The answer should have been −10-10 feet, because the sum of the absolute values of −6-6 and 44 is 1010. The answer has to be negative because the sign of the number with the larger absolute value is negative.\newline
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Read this word problem.\newlineIn science class, Antonio started an experiment using a solution with a temperature of −5 ∘C-5 \, ^{\circ}\mathrm{C}. During the experiment, the change in the solution's temperature was −4 ∘C-4 \, ^{\circ}\mathrm{C}. What was the final temperature of Antonio's solution?\newlineTo solve the problem, Antonio added −5+(−4)-5 + (-4) and came up with an answer of −9 ∘C-9 \, ^{\circ}\mathrm{C}. Is Antonio correct? Why or why not?\newlineChoices:\newline(A) Yes, Antonio is correct.\newline(B) No. The answer should have been 9 ∘C9 \, ^{\circ}\mathrm{C}, not −9 ∘C-9 \, ^{\circ}\mathrm{C}, because a negative plus a negative is always a positive.\newline(C) No. Antonio should have subtracted −5−(−4)-5 - (-4) because the temperature dropped.
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Read this word problem.\newlineThe afternoon temperature in Biscoff Bay was −2 ∘F-2 \, ^{\circ}\mathrm{F}. By midnight, a warm front moved in and the temperature rose to 11 ∘F11 \, ^{\circ}\mathrm{F}. What was the change in temperature from afternoon to midnight?\newlineTo solve the problem, Ross subtracted 11−(−2)11 - (-2) and came up with an answer of 13 ∘F13 \, ^{\circ}\mathrm{F}. Is Ross correct? Why or why not?\newlineChoices:\newline(A) Yes, Ross is correct.\newline(B) No. The answer should have been 9 ∘F9 \, ^{\circ}\mathrm{F}, not 13 ∘F13 \, ^{\circ}\mathrm{F}, because the difference between 1111 and 22 is 99.\newline(C) No. Ross should have added −2+11-2 + 11 because the temperature rose.
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