lesson 3 homework practice writing equations

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Into Math Grade 7 Module 7 Lesson 3 Answer Key Write Two-Step Equations for Situations

We included  HMH Into Math Grade 7 Answer Key  PDF   Module 7 Lesson 3 Write Two-Step Equations for Situations to make students experts in learning maths.

HMH Into Math Grade 7 Module 7 Lesson 3 Answer Key Write Two-Step Equations for Situations

I Can write two-step equations for various situations.

Spark Your Learning

Explanation: He made 6 quiches yesterday.

Scenario 2: Javier buys four dozen eggs. He saves $1.50 by using a coupon. The total he pays is $8.50. What was the cost of a dozen eggs without the coupon? Answer: $2.50

Explanation: The cost of a dozen eggs without a coupon is $2.50.

Scenario 3: Lina ate \(\frac{1}{4}\) of a quiche for lunch. Each of her two sisters split another piece equally. The three ate a total of \(\frac{7}{12}\) of the quiche. What fraction of the quiche did each of Lina’s sisters eat? Answer:

Turn and Talk Choose one of the equations you wrote. Make up another scenario that the equation could represent. Answer:

Build Understanding

C. What is the value of the expression you wrote? Answer: x = 18 feet.

D. Use your answers from Parts B and C to write an equation that can be used to find the length of each of the two equal sides. Answer:

E. How would your equation change if the perimeter were 80 feet? Answer: 80 = 2 (x + 10).

F. What would your equation be if the perimeter were 80 feet and the base were 10 feet long? Answer: The equation is 80 = 2 (x + 10). Given Perimeter = 80 feet and base = 10 feet. Let us assume one side of the traingle is x a = x feet p = 2(a + b) 80 = 2 (x + 10)

Turn and Talk How is an equation like an expression? How is it different? Answer:

Step It Out

B. Write an equation that can be used to find the unknown information. Use x as the variable. Answer: 0.5(22 + x) = 18.55

C. What does each side of the equation represent? Answer: Each side of the equation represents before the discount and after the discount given.

D. What does the variable x represent? Answer: X represents the price of the shoes before the discount.

Check Understanding

Question 1. Each time Cheryl runs, she runs 3 miles. She rides her bike only on Saturdays and always for 10 miles. She exercises the same amount each week. She rides and runs for a total of 22 miles in a week. Write an equation that can be used to find out how many times Cheryl goes running each week. Answer: 3x + 10y = 22

Explanation: An equation that can be used to find out how many times Cheryl goes running each week is 3x + 10y = 22.

Question 2. Mrs. Wu uses a 25% off coupon to buy 1 adult ticket and 1 child ticket to a movie. She pays a total amount of $9.00. A child ticket without the coupon costs $4.00. Write an equation that can be used to find the cost of an adult ticket without the coupon. Answer: cost of an adult ticket is $7.25.

Explanation: An equation that can be used to find the cost of an adult ticket without the coupon is 11.25 – 4 = $7.25

On Your Own

Model with Mathematics For Problems 3-8, write an equation to represent the situation.

Explanation: Given, Perimeter us 120inches Sides are 24 inches + 24 inches = 48 inches Two longer sides + (24 × 2) = 120 inches (2 × x)  + 48 = 120 2x = 120 – 48 2x = 72 x = 72 ÷ 2 x = 36

Question 4. Ms. Malia bought a laptop with a 10% discount. She also bought a mouse for $13.99 and spent a total of $621.49 before taxes. Write an equation to find the original cost of the laptop. Answer: $675

Explanation: The original cost of the laptop is x Given discount = 10% Price of mouse = $13.99 Total amount spent is $621.49 x – x \(\frac{10}{100}\) + 13.99 = 621.49 x – \(\frac{x}{10}\) + 13.99 = 621.99 \(\frac{9x}{10}\) + 13.99 = 621.99 \(\frac{9x}{10}\) = 621.99 -13.99 \(\frac{9x}{10}\) = 607.5 9x = 607.5 × 10 x = 6075 ÷ 9 x = $675

Question 5. Paolo is using his grandmother’s cookie recipe. He always doubles the amount of chocolate chips and oats. The recipe calls for 2\(\frac{1}{2}\) cups of chocolate chips. The total amount of chips and oats after doubling is 6\(\frac{1}{3}\) cups. Write an equation to find the original amount of oats in the recipe. Answer: x = 1 \(\frac{11}{12}\)

Explanation: Given, The total amount of chips and oats is 6\(\frac{1}{3}\) Recipe calls for 2\(\frac{1}{2}\) 6\(\frac{1}{3}\) – 2\(\frac{1}{2}\) = 2x \(\frac{19}{3}\) – \(\frac{5}{2}\) = 2x \(\frac{23}{6}\) = 2x \(\frac{23}{12}\) = x x = 1\(\frac{11}{12}\)

Explanation: Length = x + 3 Perimeter of the square = 4 × length = 54.8 4 (x + 3) = 54.8 x + 3 = 54.8 ÷ 4 x + 3 = 13.7 x = 13.7 – 3 x = 10.7 Each side of the length = 10.7

Question 7. Ms. Emily buys a hat and gloves with a coupon for 30% off her entire purchase. The gloves cost $35 before the discount. Her biH before tax is $44.80. Write an equation to find the original cost of the hat. Answer: ($35 + x) (1 – 0.3) 44.80

Question 8. Bo’s sister Anna is \(\frac{3}{4}\) his age minus 1 year. She is 11 years old. Write an equation to find Bo’s age. Answer: Bo’s age is 16.

Explanation: Let us solve the given question based on the given conditions. \(\frac{3}{4}\) × x – 1 = 11 Now solve the given equation \(\frac{3}{4}\)x = 11 + 1 \(\frac{3}{4}\)x = 12 x = 12 × \(\frac{4}{3}\) x = 16. Bo’s age is 16.

I’m in a Learning Mindset!

What barriers do I perceive to writing two-step equations for situations? Answer:

Lesson 7.3 More Practice/Homework

Question 1. Pierce is making a rectangular frame for a photo collage that has a perimeter of 72.2 inches. The length of the frame is 20.3 inches. Write an equation to find the width of the frame. Answer: x = \(\frac{79}{5}\).

Explanation: From the given question, 2(20.3 + x) = 72.2 Let us solve the equation Now expand the given expression 40.6 + 2x = 72.2 2x = 72.2 – 40.6 2x = 31.6 x = 31.6 ÷ 2 x = 79 ÷ 5

Question 2. Kendra is 3 times her daughter’s age plus 7 years. Kendra is 49 years old. Write an equation to find her daughter’s age. Answer: Her daughter’s age is 14.

Explanation: Let us solve the given question 7 + 3x = 49 3x = 49 – 7 3x = 42 Divide both sides x = 42 ÷ 3 simplify x = 14

Question 3. Mitchell orders a plain turkey sandwich and a drink for lunch. The drink is $2.95. Instead he is served the super sandwich with lettuce, tomato, and mayonnaise. The restaurant manager takes 15% off the price of the sandwich. Write an equation to determine the original price of Mitchell’s sandwich if his new bill is $8.05. Answer: Original price is $6

Explanation: The original price of the sandwich is $x. The drink is $2.95 $2.95 + (1 – 0.15) x = $8.05 $2.95 + 0.85 x = $8.05 0.85x = $8.05 -$2.95 0.85x = $5.1 x = $5.1 ÷ 0.85 x = $6

Explanation: Let us assume Bianca’s height as x. \(\frac{2}{3}\) × x + 32 = 60 \(\frac{2}{3}\) × x = 60 – 32 \(\frac{2}{3}\) × x = 28 x = (28 × 3) ÷ 2 x = 84 ÷ 2 x = 42 Therefore Bianca’s height is 42 inches.

Question 5. Health and Fitness Tyler does squats and pushups. He wants to increase the number of each type of exercise by 20% by the end of the month. He currently does 25 pushups. If Tyler meets his goal, he will do a total of 13 more squats and pushups than he does now. Write an equation to find how many squats Tyler does now. Answer: x = 40

Explanation: Let us solve the given question 25 × 20% + x × 20% = 13 5 + 0.2x = 13 0.2x = 13 – 5 0.2x = 8 x = 8 ÷ 0.2 x = 80 ÷ 2 x = 40 Therefore Tyler does 40 squats.

Question 6. Model with Mathematics An equilateral triangle has side lengths that measure x + 4 inches. The perimeter of the triangle is 18.6 inches. Write an equation to find the value of x. Answer: x = 2.2

Explanation: Given is an equilateral triangle Side is x + 4 inches Perimeter is 18.6 inches. The three sides of an equilateral traingle are equal x + 4 = 18.6 ÷ 3 x + 4 = 6.2 x = 6.2 – 4 x = 2.2

Question 7. Model with Mathematics Ms. Lynette earns $19.50 an hour when she works overtime. She worked overtime twice this week. One day she worked 3 hours of overtime. Her total overtime pay for the week is $146.25. Write an equation to find the number of overtime hours worked on the second day. Answer: 4.5 hours

Explanation: Let us assume the the number of overtime hours worked on the second day as x 3 × 19.5 + 19.5 × x = 146.25 58.5 + 19.5x = 146.25 19.5x = 146.25 -58.5 19.5x = 87.75 x = 87.75 ÷ 19.5 x = 4.5 hours

Question 8. A parallelogram has a perimeter of 50\(\frac{1}{2}\) inches. The two longer sides of the parallelogram are each 16\(\frac{1}{4}\) inches. Write an equation to find the length of each of the shorter sides. Answer:

Question 9. A baby usually gains 10% of its birth weight plus 2 pounds in the first six weeks after birth. A baby gained 2.8 pounds. Write an equation to find the baby’s birth weight. Answer: 1.1x + 2 = 2.8

Explanation: Gain 10% = 100% + 10% = 110% = 1.1 Let us assume the baby’s birth weight as x. Now let us solve the given question 1.1x + 2 = 2.8 

Question 10. A rhombus has sides of length x + 6 inches and a perimeter of 49 inches. Which equation represents this situation? (A) 4x + 6 = 49 (B) 4(x + 6) – 49 (C) x + 6 = 49 (D) x + 24 = 49 Answer: (B) 4(x + 6) – 49

Explanation: Rhombus has four equal sides Perimeter = 4 × side length = x + 6 Perimeter = 49 inches Side = x + 6 4 (x + 6) = 49

Question 11. Mrs. Owens has a coupon for 40% off a pair of shoes. She pays $111.79 for a pair of shoes and a dress after using the coupon. The dress costs $64.99. Which equation can be solved for x, the retail price of the shoes? (A) 0.6x + 64.99 = 111.79 (B) 0.4x + 64.99 = 111.79 (C) 0.6(x + 64.99) = 111.79 (D) 0.4(x + 64.99) = 111.79 Answer: (A) 0.6x + 64.99 = 111.79

Explanation: From the given question Calculate the given question (64.99 + 40% of x) × (1 – 40%) = 111.79 0.6x + 64.99 = 111.79

Spiral Review

Question 12. Sarah began the school week with $2.60 in her lunch account. She deposited $20 on Monday, and then spent $4.75 each day that week for lunch. What was the balance in her lunch account at the end of the day on Friday? Answer: -1.15

Explanation: Based on the given question calculate 2.6 + 20 – 4.75 × 5 2.6 + 20 – 23.75 22.6 – 23.75 -1.15 The balance in her lunch account at the end of the day on Friday is -1.15.

Question 13. Mr. Alvarado goes shopping at the mall with $70. He buys a pair of pants for $33.76 and a shirt for $29.52. He also returns a hat he bought the previous week for $19.67. How much money does Mr. Alvarado have after he buys the pants and shirt and returns the hat? Answer: $26.39

Explanation: Mr. Alvarado went for shopping with $70. Pair of pants for $33.76 The hat he brought = $19.67 The money Mr. Alvarado  have is 70 – 29.52 – 33.76 + 19.67 = 26.39

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Unit 3: Linear relationships

Lesson 3: representing proportional relationships.

• Graphing proportional relationships: unit rate (Opens a modal)
• Graphing proportional relationships from a table (Opens a modal)
• Graphing proportional relationships from an equation (Opens a modal)
• Graphing proportional relationships Get 3 of 4 questions to level up!

Lesson 4: Comparing proportional relationships

• Rates & proportional relationships example (Opens a modal)
• Rates & proportional relationships: gas mileage (Opens a modal)
• Rates & proportional relationships Get 5 of 7 questions to level up!

Lesson 7: Representations of linear relationships

• Linear & nonlinear functions: missing value (Opens a modal)

Lesson 8: Translating to y=mx+b

• Intro to slope-intercept form (Opens a modal)
• Graph from slope-intercept equation (Opens a modal)

Lesson 9: Slopes don't have to be positive

• Intro to intercepts (Opens a modal)
• Slope-intercept equation from slope & point (Opens a modal)
• Linear & nonlinear functions: word problem (Opens a modal)
• Intercepts from a graph Get 3 of 4 questions to level up!
• Slope from graph Get 3 of 4 questions to level up!
• Slope-intercept intro Get 3 of 4 questions to level up!
• Graph from slope-intercept form Get 3 of 4 questions to level up!
• Slope-intercept equation from graph Get 3 of 4 questions to level up!

Lesson 10: Calculating slope

• No videos or articles available in this lesson
• Slope from two points Get 3 of 4 questions to level up!

Lesson 11: Equations of all kinds of lines

• Converting to slope-intercept form (Opens a modal)

Extra practice: Slope

• Intro to slope (Opens a modal)
• Worked examples: slope-intercept intro (Opens a modal)
• Graphing slope-intercept form (Opens a modal)
• Writing slope-intercept equations (Opens a modal)
• Slope-intercept form review (Opens a modal)
• Slope-intercept from two points Get 3 of 4 questions to level up!

Lesson 12: Solutions to linear equations

• Solutions to 2-variable equations (Opens a modal)
• Worked example: solutions to 2-variable equations (Opens a modal)
• Solutions to 2-variable equations Get 3 of 4 questions to level up!

Lesson 13: More solutions to linear equations

• Completing solutions to 2-variable equations (Opens a modal)
• Complete solutions to 2-variable equations Get 3 of 4 questions to level up!

Extra practice: Intercepts

• x-intercept of a line (Opens a modal)
• Intercepts from an equation (Opens a modal)
• Worked example: intercepts from an equation (Opens a modal)
• Intercepts of lines review (x-intercepts and y-intercepts) (Opens a modal)
• Intercepts from an equation Get 3 of 4 questions to level up!

Chapter 8, Lesson 3: Writing Two-Step Equations

• Extra Examples
• Personal Tutor
• Self-Check Quizzes

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