mcgraw hill lesson 8 problem solving reasonable answers

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Math Connects: Concepts, Skills, and Problem Solving Course 3, Grade: 8 Publisher: Glencoe/McGraw-Hill

Math connects: concepts, skills, and problem solving course 3, title : math connects: concepts, skills, and problem solving course 3, publisher : glencoe/mcgraw-hill, isbn : 78740509, isbn-13 : 9780078740503, use the table below to find videos, mobile apps, worksheets and lessons that supplement math connects: concepts, skills, and problem solving course 3., textbook resources.

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McGraw Hill My Math Grade 3 Chapter 9 Lesson 8 Answer Key Solve Two-Step Word Problems

All the solutions provided in  McGraw Hill My Math Grade 3 Answer Key PDF Chapter 9 Lesson 8 Solve Two-Step Word Problems will give you a clear idea of the concepts.

McGraw-Hill My Math Grade 3 Answer Key Chapter 9 Lesson 8 Solve Two-Step Word Problems

Sometimes in order to solve a problem you need to do more than one step or use more than one operation.

So, 5 × $6 + $7 = $____________. The unknown is $ ____________. Gustavo spent $____________ on tools. Check: Use mental math to check your answer for reasonableness. Gustavo had $37 and spent $7. $37 – $7 = $ ______________ Since $30 ÷ 5 tools = $_____________ each, the answer is reasonable. Answer: Gustavo spent $37 on tools

Explanation: Checking, Gustavo had $37 and spent $7. $37 – $7 = $30 Since $30 ÷ 5 tools = $6 So, the answer is reasonable.

Explanation: For instance, in a division problem like 424 ÷ 4 − 10, we can check is our answer is reasonable or not, by estimating an approximate answer or by using the division formula. We can round down 424 to the nearest hundreds, to estimate the answer. That will be 400.

Guided Practice

Write an equation with a letter for the unknown. Then solve. Check for reasonableness.

Question 1. A city bus had 14 passengers. At a stop, 5 people got off and 8 people got on. How many people are on the bus now? Answer: There are 17 people on the bus.

Explanation: Given, A city bus had 14 passengers. At a stop, 5 people got off and 8 people got on. Let the unknown be y , The equation will be, 14 + 8 – 5 = y y = 17 So, There are 17 people on the bus.

Question 2. Grandmother picked 4 times as many apples as pears. What is the difference in the number of apples and pears picked if she picked 8 pears? Answer: the difference in the number of apples and pears is 24.

Explanation: Given, Grandmother picked 4 times as many apples as pears. the difference in the number of apples and pears picked if she picked 8 pears is let the unknown be y , y = 4 × 8 = 32 Then she has 32 apples and 8 pears That means 32 – 8 = 24 So, the difference in the number of apples and pears is 24.

Independent Practice

Algebra Write an equation with a letter for the unknown. Then solve. Check for reasonableness.

Question 3. Whitney went to the hobby store. She bought 3 model airplanes for $4 each. She received $8 in change. How much money did she start with? Answer: She has $20 from the start

Explanation: Given, Whitney went to the hobby store. She bought 3 model airplanes for $4 each. let the unknown be y 3 × 4  = y y = 12 She received $8 in change. Then $20 – $12 = $8 She has $20 from the start

check  $12 + $8 = $20 .

Question 4. Mr. Robbins gave 9 students one pencil each. That afternoon, he gave 5 more students one pencil each. Now he has 15 pencils. How many pencils did he start with? Answer: He started with 29 pencils

Explanations: Given, Mr. Robbins gave 9 students one pencil each. That afternoon, he gave 5 more students one pencil each. Now he has 15 pencils. let the unknown be y , 9 + 5 + 15 = y y = 29 He started with 29 pencils

Check,  9 + 5 + 15 = 29.

Explanation: Given, Pamela has 7 pens. Cesar has 9 pens, Carmen has 20 pens Pamela and Cesar together have 7 + 9 = 16 Carmen has 20 pens , then , 20 – 16 = 4 So, Carmen have 4 more pens than Pamela and Cesar have together.

Algebra Circle the correct equation. Then solve the problem.

Question 6. Molly earns $10 each week for babysitting. She spends $3 of that each week and saves the rest. How much money does she save after 8 weeks? ($10 – $3) × 8 = m $10 – $3 × 8 = m Answer:  Molly has $56 after 8 weeks.

Explanation: Given, Molly earns $10 each week for babysitting. She spends $3 of that each week and saves the rest. The the equation will be , ($10 – $3) × 8 = m Here, m is the unknown The parentheses are to differentiate between the money spent on each week. 7 × 8 = m m = 56. So, Molly has $56 after 8 weeks.

Question 7. The first 5 pages of Angel’s photo album are filled with 8 photos each. The next page has only 7 photos. How many photos are on the 6 pages? 5 × 8 + 7 = p 5 × 8 + p = 40 Answer: There are 47 photos on the 6 pages.

Explanation: Given, The first 5 pages of Angel’s photo album are filled with 8 photos each. The next page has only 7 photos. The equation will be, 5 × 8 + 7 = p 40 + 7 = p p = 47 So, There are 47 photos on the 6 pages.

Algebra Find each unknown.

Question 8. k – 9 = 9 k = _____________ Answer: 18

Explanation: Given, k – 9 = 9 k = 9 + 9 = 18 So, k = 18.

Question 9. 45 ÷ v = 5 v = ______________ Answer: 9

Explanation: Given, 45 ÷ v = 5 v = 45 ÷ 5 = 9 So, v= 9

Question 10. 9 + 2 = 12 – q q = _____________ Answer: 1

Explanation: Given, 9 + 2 = 12 – q q = 12 – 11 = 1 So, q = 1.

Problem Solving

Mathematical PRACTICE Check for Reasonableness Write an equation with a letter for the unknown. Then solve. Check for reasonableness.

Question 11. It rained 6 inches each month for the last 6 months. How much will it need to rain this month for the total rainfall to be 43 inches? Answer: The rainfall of this month should be 7 inches.

Explanation: Given, It rained 6 inches each month for the last 6 months. Then expression is 6 × 6 = 36 Let the unknown be y , ( 6× 6 ) + y = 43 36 + y = 43 y = 43 – 36 y = 7 So, The rainfall of this month should be 7 inches. check, replace y = 7 36 + y = 43 36 + 7 = 43 43 = 43. So, the answer is reasonable.

Question 12. There were 48 oranges in 6 equal layers in a box. Mother took some oranges from the top layer for snacks. How many oranges did mother take if there are 5 oranges left on the top layer? Answer:  the mother took 3 oranges.

Explanation: Given, There were 48 oranges in 6 equal layers in a box. Mother took some oranges from the top layer for snacks. Then, each layer has 8 oranges, if there are 5 oranges on the top layer then, let the unknown be y , (48  ÷ 6) – y = 5 8 – y = 5 y = 3 So, the mother took 3 oranges.

check, y = 3 8 – y = 5 8 – 3 = 5 5 = 5 So, The answer is reasonable.

HOT Problems

Question 13. Mathematical PRACTICE Make Sense of Problems Amelia made 10 fruit kabobs. She divided 20 cherries equally among half of the kabobs. How many cherries did each kabob get? Answer:  Each kabob gets 4 cherries.

Explanation: Given, Amelia made 10 fruit kabobs. She divided 20 cherries equally among half of the kabobs. then, 20  ÷ ( 10  ÷ 2 )  = y 20  ÷  5 = y y = 4. So, Each kabob gets 4 cherries.

Question 14. Mathematical PRACTICE Find the Error Look back at Exercise 6. Explain why the other choice is incorrect. Answer:  Because There are no parentheses for $10 – $3 × 8 = m.

Explanation: Given, Molly earns $10 each week for babysitting. She spends $3 of that each week and saves the rest. The the equation will be , ($10 – $3) × 8 = m Here, m is the unknown The parentheses are to differentiate between the money spent on each week. 7 × 8 = m m = 56. So, Molly has $56 after 8 weeks.

Question 15. Building on the Essential Question Why is it important to perform the operations in an equation in a certain order? Answer: Subtraction, multiplication, and division are all examples of operations.) The order of operations is important because it guarantees that people can all read and solve a problem in the same way.

Explanation: for example, (48  ÷ 6) – y = 5 8 – y = 5 y = 3 Here, the order is solve with in parentheses first. and then for the mathematical operations.

McGraw Hill My Math Grade 3 Chapter 9 Lesson 8 My Homework Answer Key

Question 1. 48 ÷ 6 + m = 11 m = ______________ Answer: m = 3.

Explanation: Given, 48 ÷ 6 + m = 11 8 + m = 11 m = 11 – 8 = 3 So, m = 3.

Question 2. 37 – 9 = h × 4 h = ________________ Answer: h = 7

Explanation: Given, 37 – 9 = h × 4 28 = h × 4 h = 28 ÷ 4 = 7 So, h = 7.

Question 3. 20 + 20 = 4 × w w = _________________ Answer: w = 10

Explanation: Given, 20 + 20 = 4 × w 40 = 4 × w w = 40 ÷ 4 = 10 So, w = 10

Question 4. (4 + 2) × r = 54 r = __________________ Answer: r = 9

Explanation: Given, (4 + 2) × r = 54 6 × r = 54 r = 54 ÷ 6 = 9 So, r = 9

Question 5. The football team had its photo taken. There are 3 rows of 8 players each. The fourth row has 6 players. How many players are in the team photo? Answer: There are 30 players in the team photo.

Explanation: Given, The football team had its photo taken. There are 3 rows of 8 players each. The fourth row has 6 players. The equation will be ( 3 × 8 ) + 6 = y Let the y be the unknown 24 + 6 = y y = 30 So, There are 30 players in the team photo.

check, y= 30 ( 3 × 8 ) + 6 = y ( 3 × 8 ) + 6 = 30 24 + 6 = 30 30 = 30 So, the answer is reasonable.

Question 6. Mrs. Dove made 15 pancakes. She divided them evenly among Kurt, Joan, and David. Kurt and Joan ate all of their pancakes, but David did not eat some of his. There were 2 pancakes left on David’s plate. How many pancakes did he eat? Answer: David ate 3 pancakes

Explanation: Given, Mrs. Dove made 15 pancakes. She divided them evenly among Kurt, Joan, and David. Kurt and Joan ate all of their pancakes, There were 2 pancakes left on David’s plate. Let the unknown be y ( 15 ÷ 3 ) – 2 = y 5 – 2 = y y = 3 So, David ate 3 pancakes

Check, y = 3 5 – 2 = y 5 – 2 = 3 3 = 3 so, The answer is reasonable.

Question 7. Keira has 83 spelling words to study in 8 weeks. She already knows 3 words. She will study the same number of words each week. How many spelling words will Keira study each week? Answer: 10

Explanation: Given, Keira has 83 spelling words to study in 8 weeks. She already knows 3 words. She will study the same number of words each week. Let the unknown be y (83 – 3 ) ÷ 8 = y y = 80 ÷ 8 y = 10 So, She has to read 10 spelling words each week.

check, y = 10 y = 80 ÷ 8 10 = 80 ÷ 8 10 = 10. So, The answer is reasonable.

Question 8. Grant bought 6 packs of stickers for $2 each. How much change will Grant receive if he pays with three $5 bills? Answer: $3

Explanation: Given, Grant bought 6 packs of stickers for $2 each. 6 × 2 = 12 if he pays with three $5 bills 3 × 5 = 15 He receives 15 – 12 = 3 So, Grant receives the change of $3.

Test Practice

Question 9. Isaac has taken five quizzes. He scored 8 points on each of the first 4 quizzes. He scored y points on the fifth quiz. He has scored a total of 41 points. Which equation represents the situation? (A) 41 ÷ 5 = y (B) 8 × 4 ÷ 5 = y (C) 4 × 8 + y = 41 (D) 41 ÷ 4 + y = 8 Answer: C

Explanation: Given, Isaac has taken five quizzes. He scored 8 points on each of the first 4 quizzes. He scored y points on the fifth quiz. He has scored a total of 41 points. Let the unknown be y 4 × 8 + y = 41 32 + y = 41 y = 41 – 32 y = 9. So, Option C is correct option.

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