\nThe ages of three sisters are consecutive integers. The sum of their ages is 45. Calculate their ages.
\na. Use a tape diagram to find their ages.
\nAnswer:
\n
![\"Engage](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Engage-NY-Math-7th-Grade-Module-3-Lesson-7-Example-Answer-Key-1.png\")
<\/p>\nExample
\nThe ages of three sisters are consecutive integers. The sum of their ages is 45. Calculate their ages.
\na. Use a tape diagram to find their ages.
\nAnswer:
\n<\/p>\n
45-3=42
\n42\u00f73=14<\/p>\n
Youngest sister: 14 years old b. If the youngest sister is x years old, describe the ages of the other two sisters in terms of x, write an expression for the sum of their ages in terms of x, and use that expression to write an equation that can be used to find their ages. c. Determine if your answer from part (a) is a solution to the equation you wrote in part (b). Your brother is going away to college, so you no longer have to share a bedroom. You decide to redecorate a wall by hanging two new posters on the wall. The wall is 14 feet wide, and each poster is four feet wide. You want to place the posters on the wall so that the distance from the edge of each poster to the nearest edge of the wall is the same as the distance between the posters, as shown in the diagram below. Determine that distance. Your parents are redecorating the dining room and want to place two rectangular wall sconce lights that are 25 inches wide along a 10 \\(\\frac{2}{3}\\)-foot wall so that the distance between the lights and the distances from each light to the nearest edge of the wall are all the same. Design the wall and determine the distance. Let the distance between a light and the nearest edge of a wall be x ft. Write an expression in terms of x for the total length of the wall. Then, use the expression and the length of the wall given in the problem to write an equation that can be used to find that distance. Now write an equation where y stands for the number of inches: Let the distance between a light and the nearest edge of a wall be y inches. Write an expression in terms of y for the total length of the wall. Then, use the expression and the length of the wall to write an equation that can be used to find that distance (in inches). What value(s) of y makes the second equation true: 24, 25, or 26? Since substituting 26 for y results in a true equation, the distance between the light and the nearest edge of the wall should be 26 in.<\/p>\n Sophia pays a $19.99 membership fee for an online music store. b. If Sophia purchases n songs for $0.99 each, write an expression for the total cost. c. Sophia\u2019s friend has saved $118 but is not sure how many songs she can afford if she buys the membership and some songs. Use the expression in part (b) to write an equation that can be used to determine how many songs Sophia\u2019s friend can buy. d. Using the equation written in part (c), can Sophia\u2019s friend buy 101, 100, or 99 songs? Question 1. b. 9m-19=3m+1 m=\\(\\frac{10}{3}\\) c. 3(y+8)=2y-6 y=30 Question 2. b. Is -4 a solution to the equation? Why or why not? c. Is -3 a solution to the equation? Why or why not? d. What is the mystery number? Question 3. b. Let n represent the smallest integer. Write an equation that can be used to find the smallest integer. c. Determine if each value of n below is a solution to the equation in part (b). Question 4. a. Her first guess is 30. Is she correct? Why or why not? b. Her second guess is 2. Is she correct? Why or why not? c. Her final guess is 4 \\(\\frac{1}{2}\\). Is she correct? Why or why not? Question 1. b. 3x-1=5x+10 x=-5 \\(\\frac{1}{2}\\) Question 2. b. Let the cost of a pen be p dollars. Write an expression for the total cost of four pens and seven mechanical pencils in terms of p. c. Write an equation that could be used to find the cost of a pen. d. Determine a value for p for which the equation you wrote in part (b) is true. e. Determine a value for p for which the equation you wrote in part (b) is false. Engage NY Eureka Math 7th Grade Module 3 Lesson 7 Answer Key Eureka Math Grade 7 Module 3 Lesson 7 Example Answer Key Example The ages of three sisters are consecutive integers. The sum of their ages is 45. Calculate their ages. a. Use a tape diagram to find their ages. Answer: 45-3=42 42\u00f73=14 Youngest … Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/79229"}],"collection":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/comments?post=79229"}],"version-history":[{"count":1,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/79229\/revisions"}],"predecessor-version":[{"id":137640,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/79229\/revisions\/137640"}],"wp:attachment":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media?parent=79229"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/categories?post=79229"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/tags?post=79229"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n2nd<\/sup> sister: 15 years old
\nOldest sister: 16 years old<\/p>\n
\nAnswer:
\nYoungest sister: x years old
\n2nd sister: (x+1) years old
\nOldest sister: (x+2) years old
\nSum of their ages: x+(x+1)+(x+2)
\nEquation: x+(x+1)+(x+2)=45<\/p>\n
\nAnswer:
\nx+(x+1)+(x+2)=45
\n14+(14+1)+(14+2)=45
\n45=45
\nTrue
\n\u2192 Let x be an integer; write an algebraic expression that represents one more than that integer.
\n\u2192 x+1
\n\u2192 Write an algebraic expression that represents two more than that integer.
\n\u2192 x+2
\nDiscuss how the unknown unit in a tape diagram represents the unknown integer, represented by x. Consecutive integers begin with the unknown unit; then, every consecutive integer thereafter increases by 1 unit.<\/p>\nEureka Math Grade 7 Module 3 Lesson 7 Opening Exercise Answer Key<\/h3>\n
\n![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-Grade-7-Module-3-Lesson-7-Opening-Exercise-Answer-Key-2.png\")
\nAnswer:
\n14-4-4=6
\n6\u00f73=2
\nThe distance is 2 feet<\/p>\n
\n![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-Grade-7-Module-3-Lesson-7-Opening-Exercise-Answer-Key-3.png\")
\nAnswer:
\n25 in. = \\(\\frac{25}{12}\\) ft. = 2 \\(\\frac{1}{12}\\) ft.
\n(10 \\(\\frac{2}{3}\\) ft. – 2 \\(\\frac{1}{12}\\) ft. – 2 \\(\\frac{1}{12}\\) ft.) \u00f7 3
\n(10 \\(\\frac{8}{12}\\) ft. – 2 \\(\\frac{1}{12}\\) ft. – 2 \\(\\frac{1}{12}\\) ft.) \u00f7 3
\n(6 \\(\\frac{6}{12}\\) ft.) \u00f7 3
\n6 \\(\\frac{1}{2}\\) ft. \u00f7 3
\n\\(\\frac{13}{2}\\) ft. \u00f7 3
\n\\(\\frac{13}{2}\\) ft. \u00d7 \\(\\frac{1}{3}\\)
\n\\(\\frac{13}{6}\\) ft.
\n2 \\(\\frac{1}{6}\\) ft.
\nOR
\n10 \\(\\frac{2}{3}\\) ft.
\n10 ft.\u00d712 \\(\\frac{in}{ft.}\\) + \\(\\frac{2}{3}\\) ft. \u00d7 12 \\(\\frac{in}{ft}\\)
\n120 in. + 8 in.
\n128 in.
\n(128 in. – 25 in. – 25 in.) \u00f7 3
\n78 in. \u00f7 3
\n26 in.<\/p>\n
\nAnswer:
\n3x+2 \\(\\frac{1}{12}\\)+2 \\(\\frac{1}{12}\\)
\n3x+2 \\(\\frac{1}{12}\\)+2 \\(\\frac{1}{12}\\)=10 \\(\\frac{2}{3}\\)<\/p>\n
\nAnswer:
\n2 \\(\\frac{1}{12}\\) feet =25 inches; therefore, the expression is 3y+25+25.
\n10 \\(\\frac{2}{3}\\) feet =128 inches; therefore, the equation is 3y+25+25=128.<\/p>\n
\nAnswer:
\ny=24
\n3y+25+25=128
\n3(24)+25+25=128
\n72+25+25=128
\n122=128
\nFalse
\ny=25
\n3y+25+25=128
\n3(25)+25+25=128
\n75+25+25=128
\n125=128
\nFalse
\ny=26
\n3y+25+25=128
\n3(26)+25+25=128
\n78+25+25=128
\n128=128
\nTrue<\/p>\nEureka Math Grade 7 Module 3 Lesson 7 Exercise Answer Key<\/h3>\n
\na. If she also buys two songs from a new album at a price of $0.99 each, what is the total cost?
\nAnswer:
\n$21.97<\/p>\n
\nAnswer:
\n0.99n+19.99<\/p>\n
\nAnswer:
\n0.99n+19.99=118<\/p>\n
\nAnswer:
\nn=99
\n0.99n+19.99=118
\n0.99(99)+19.99=118
\n98.01+19.99=118
\n118=118
\nTrue
\nn=100
\n0.99n+19.99=118
\n0.99(100)+19.99=118
\n99+19.99=118
\n118.99=118
\nFalse
\nn=101
\n0.99n+19.99=118
\n0.99(101)+19.99=118
\n99.99+19.99=118
\n119.98=118
\nFalse<\/p>\nEureka Math Grade 7 Module 3 Lesson 7 Problem Set Answer Key<\/h3>\n
\nCheck whether the given value is a solution to the equation.
\na. 4n-3=-2n+9 n=2
\nAnswer:
\n4(2)-3=-2(2)+9
\n8-3=-4+9
\n5=5
\nTrue<\/p>\n
\nAnswer:
\n9(\\(\\frac{10}{3}\\))-19=3(\\(\\frac{10}{3}\\))+1
\n\\(\\frac{90}{3}\\)-19=30\/3+1
\n30-19=10+1
\n11=11
\nTrue<\/p>\n
\nAnswer:
\n3(30+8)=2(30)-6
\n3(38)=60-6
\n114=54
\nFalse<\/p>\n
\nTell whether each number is a solution to the problem modeled by the following equation.
\nMystery Number: Five more than -8 times a number is 29. What is the number?
\nLet the mystery number be represented by n.
\nThe equation is 5+(-8)n=29.
\na. Is 3 a solution to the equation? Why or why not?
\nAnswer:
\nNo, because 5-24\u226029.<\/p>\n
\nAnswer:
\nNo, because 5+32\u226029.<\/p>\n
\nAnswer:
\nYes, because 5+24=29.<\/p>\n
\nAndrew:
\n-3 because 5 more than -8 times -3 is 29.<\/p>\n
\nThe sum of three consecutive integers is 36.
\na. Find the smallest integer using a tape diagram.
\nAnswer:
\n![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/03\/Eureka-Math-Grade-7-Module-3-Lesson-7-Problem-Set-Answer-Key-20.png\")
\n36-3=33
\n33\u00f73=11
\nThe smallest integer is 11.<\/p>\n
\nAnswer:
\nSmallest integer: n
\n2nd<\/sup> integer: (n+1)
\n3rd<\/sup> integer: (n+2)
\nSum of the three consecutive integers: n+(n+1)+(n+2)
\nEquation: n+(n+1)+(n+2)=36.<\/p>\n
\nn=12.5
\nAnswer:
\nNo, it is not an integer and does not make a true equation.
\nn=12
\nAnswer:
\nNo, it does not make a true equation.
\nn=11
\nAnswer:
\nYes, it makes a true equation.<\/p>\n
\nAndrew is trying to create a number puzzle for his younger sister to solve. He challenges his sister to find the mystery number. \u201cWhen 4 is subtracted from half of a number, the result is 5.\u201d The equation to represent the mystery number is \\(\\frac{1}{2}\\) m-4=5. Andrew\u2019s sister tries to guess the mystery number.<\/p>\n
\nAnswer:
\nNo, it does not make a true equation.
\n\\(\\frac{1}{2}\\) (30)-4=5
\n15-4=5
\n11=5
\nFalse<\/p>\n
\nAnswer:
\nNo, it does not make a true equation.
\n\\(\\frac{1}{2}\\) (2)-4=5
\n1-4=5
\n-3=5
\nFalse<\/p>\n
\nAnswer:
\nNo, it does not make a true equation.
\n\\(\\frac{1}{2}\\) (4 \\(\\frac{1}{2}\\))-4=5
\n2 \\(\\frac{1}{4}\\)-4=5
\n-1 \\(\\frac{3}{4}\\)=5
\nFalse<\/p>\nEureka Math Grade 7 Module 3 Lesson 7 Exit Ticket Answer Key<\/h3>\n
\nCheck whether the given value of x is a solution to the equation. Justify your answer.
\na. \\(\\frac{1}{3}\\) (x+4)=20 x=48
\nAnswer:
\n(\\(\\frac{1}{3}\\) (48+4)=20
\n\\(\\frac{1}{3}\\) (52)=20
\nFalse, 48 is NOT a solution to \\(\\frac{1}{3}\\) (x+4)=20.
\n17 \\(\\frac{1}{3}\\)=20<\/p>\n
\n(3(-5 \\(\\frac{1}{2}\\))-1=5(-5 \\(\\frac{1}{2}\\))+10
\n–\\(\\frac{33}{2}\\)-1=-\\(\\frac{55}{2}\\)+10
\nTrue, -5 \\(\\frac{1}{2}\\) is a solution to 3x-1=5x+10.
\n–\\(\\frac{35}{2}\\)=-\\(\\frac{35}{2}\\)<\/p>\n
\nThe total cost of four pens and seven mechanical pencils is $13.25. The cost of each pencil is 75 cents.
\na. Using an arithmetic approach, find the cost of a pen.
\nAnswer:
\n(13.25-7(0.75))\u00f74
\n(13.25-5.25)\u00f74
\n8\u00f74
\n2
\nThe cost of a pen is $2.<\/p>\n
\nAnswer:
\n4p+7(0.75) or 4p+5.25<\/p>\n
\nAnswer:
\n4p+7(0.75)=13.25 or 4p+5.25=13.25<\/p>\n
\nAnswer:
\n4p+5.25=13.25
\n4(2)+5.25=13.25
\n8+5.25=13.25
\nTrue, when p=2, the equation is true.
\n13.25=13.25<\/p>\n
\nAnswer:
\nAny value other than 2 will make the equation false.<\/p>\n","protected":false},"excerpt":{"rendered":"