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Eureka Math Grade 4 Module 3 Lesson 12 Answer Key

Engage ny eureka math 4th grade module 3 lesson 12 answer key, eureka math grade 4 module 3 lesson 12 problem set answer key.

Use the RDW process to solve the following problems.

Question 1. The table shows the cost of party favors. Each party guest receives a bag with 1 balloon, 1 lollipop, and 1 bracelet. What is the total cost for 9 guests?

Explanation: Given each party guest receives a bag with 1 balloon, 1 lollipop, and 1 bracelet, So each guest costs 26¢ + 14¢ + 33 ¢ = 73¢, Now the total cost for 9 guests is 9 X 73¢ = 657¢ as shown in the picture above.

Explanation: Given the Turner family uses 548 liters of water per day. The Hill family uses 3 times as much water per day, So per day Hill family uses 3 X 548 liters = 1,644 liters, So number of liters of water does the Hill family use per week is 7 X 1,644 liters = 11,508 liters as shown in the picture above.

Explanation: Given Jayden has 347 marbles. Elvis has 4 times as many as Jayden. So Elvis have 4 X 347 marbles = 1,388 marbles, Now Presley has 799 fewer than Elvis means number of marbles Presley have are 1,388 – 799 = 589 marbles as shown in the picture above.

Explanation: Wrote an equation that would allow someone to find the value of R as R + $239 = $1,167 X 3, R = ($1,167 X 3) – $239.

b. Write your own word problem to correspond to the tape diagram, and then solve Answer: Joy brought 3 books each of cost $1,167, all the 3 books cost $239 more than her existing books, What is the cost of existing books? Joy’s existing books cost $3,262,

Explanation: Wrote my own word problem to correspond to the tape diagram, and then solved as below, Joy brought 3 books each of cost $1,167, all the 3 books cost $239 more than her existing books, What is the cost of existing books? Solution :        2,2 $1,167 X     3 $3,501 Now $3,501 – $239 = $3,262, So Joy’s existing books cost $3,262.

Eureka Math Grade 4 Module 3 Lesson 12 Exit Ticket Answer Key

Use the RDW process to solve the following problem.

Explanation: Given Jennifer has 256 beads. Stella has 3 times as many beads as Jennifer. So stella have 3 X 256 beads = 768 beads, Now Tiah has 104 more beads than Stella, So number of beads does Tiah have are 768 beads + 104 beads = 872 beads as shown above.

Eureka Math Grade 4 Module 3 Lesson 12 Homework Answer Key

Question 1. The table shows the number of stickers of various types in Chrissy’s new sticker book. Chrissy’s six friends each own the same sticker book. How many stickers do Chrissy and her six friends have altogether?

Explanation: Given Jared sold 194 Boy Scout chocolate bars. Matthew sold three times as many as Jared. So Matthew sold 194 X 3 =    2,1 194 X 3 582, Now Gary sold 297 fewer than Matthew. So number of bars did Gary sell are 582 – 297 = 285, therefore Gary sells 285 Boy Scout chocolate bars as shown above.

Explanation: Wrote an equation that would allow someone to find the value of M as M = (723 meters X 3) +  973 meters.

b. Write your own word problem to correspond to the tape diagram, and then solve. Answer: Peter has 2 rope pieces of one piece of length 973 meters and other 3 times 723 meters of length altogether howm much length of rope in meters do Peter have?

Peter have altogether rope of length 3,142 meters,

Explanation: Wrote my own word problem to correspond to the tape diagram, and then solved as below, Peter has 2 rope pieces of one piece of length 973 meters and other 3 times 723 meters of length altogether howm much length of rope in meters do Peter have? Solution : One piece of length is 723 meters X 3 = 723 X 3 2,169 meters, Now adding this to other piece of length 973 meters , 2,169 + 973 = 3,142 meters, therefore Peter have altogether rope of length 3,142 meters.

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4th grade (Eureka Math/EngageNY)

Unit 1: module 1: place value, rounding, and algorithms for addition and subtraction, unit 2: module 2: unit conversions and problem solving with metric measurement, unit 3: module 3: multi-digit multiplication and division, unit 4: module 4: angle measure and plane figures, unit 5: module 5: fraction equivalence, ordering, and operations, unit 6: module 6: decimal fractions, unit 7: module 7: exploring measurement with multiplication.

( 3 , 2 ) ( 3 , 2 )

( 2 , 3 ) ( 2 , 3 )

( 3 , 4 ) ( 3 , 4 )

( 5 , −4 ) ( 5 , −4 )

no solution

infinitely many solutions

ⓐ no solution, inconsistent, independent ⓑ one solution, consistent, independent

( 6 , 1 ) ( 6 , 1 )

( −3 , 5 ) ( −3 , 5 )

( 2 , 3 2 ) ( 2 , 3 2 )

( − 1 2 , −2 ) ( − 1 2 , −2 )

( 2 , −1 ) ( 2 , −1 )

( −2 , 3 ) ( −2 , 3 )

( 1 , 3 ) ( 1 , 3 )

( 4 , −3 ) ( 4 , −3 )

( 6 , 2 ) ( 6 , 2 )

( 1 , −2 ) ( 1 , −2 )

ⓐ Since both equations are in standard form, using elimination will be most convenient. ⓑ Since one equation is already solved for x , using substitution will be most convenient.

ⓐ Since one equation is already solved for y , using substitution will be most convenient. ⓑ Since both equations are in standard form, using elimination will be most convenient.

160 policies

Mark burned 11 calories for each minute of yoga and 7 calories for each minute of jumping jacks.

Erin burned 11 calories for each minute on the rowing machine and 5 calories for each minute of weight lifting.

The angle measures are 55 and 35.

The angle measures are 5 and 85.

The angle measures are 42 and 138.

The angle measures are 66 and 114.

The length is 60 feet and the width is 35 feet.

The length is 60 feet and the width is 38 feet.

It will take Clark 4 hours to catch Mitchell.

It will take Sally 1 1 2 1 1 2 hours to catch up to Charlie.

The rate of the boat is 11 mph and the rate of the current is 1 mph.

The speed of the canoe is 7 mph and the speed of the current is 1 mph.

The speed of the jet is 235 mph and the speed of the wind is 30 mph.

The speed of the jet is 408 mph and the speed of the wind is 24 mph.

206 adults, 347 children

42 adults, 105 children

13 dimes and 29 quarters

19 quarters and 51 nickels

3 pounds peanuts and 2 pounds cashews

10 pounds of beans, 10 pounds of ground beef

120 ml of 25% solution and 30 ml of 50% solution

125 ml of 10% solution and 125 ml of 40% solution

$42,000 in the stock fund and $8000 in the savings account

$1750 at 11% and $5250 at 13%

Bank $4,000; Federal $14,000

$41,200 at 4.5%, $24,000 at 7.2%

ⓐ C ( x ) = 15 x + 25 , 500 C ( x ) = 15 x + 25 , 500

ⓑ R ( x ) = 32 x R ( x ) = 32 x

ⓓ 1,500 1,500 ; when 1,500 benches are sold, the cost and revenue will be both 48,000

ⓐ C ( x ) = 120 x + 150,000 C ( x ) = 120 x + 150,000

ⓑ R ( x ) = 170 x R ( x ) = 170 x

ⓓ 3,000 3,000 ; when 3,000 benches are sold, the revenue and costs are both $510,000

( 2 , −1 , 3 ) ( 2 , −1 , 3 )

( −2 , 3 , 4 ) ( −2 , 3 , 4 )

( −3 , 4 , −2 ) ( −3 , 4 , −2 )

( −2 , 3 , −1 ) ( −2 , 3 , −1 )

infinitely many solutions ( x , 3 , z ) ( x , 3 , z ) where x = z − 3 ; y = 3 ; z x = z − 3 ; y = 3 ; z is any real number

infinitely many solutions ( x , y , z ) ( x , y , z ) where x = 5 z − 2 ; y = 4 z − 3 ; z x = 5 z − 2 ; y = 4 z − 3 ; z is any real number

The fine arts department sold 75 adult tickets, 200 student tickets, and 75 child tickets.

The soccer team sold 200 adult tickets, 300 student tickets, and 100 child tickets.

ⓐ [ 3 8 −3 2 5 −3 ] [ 3 8 −3 2 5 −3 ] ⓑ [ 2 −5 3 8 3 −1 4 7 1 3 2 −3 ] [ 2 −5 3 8 3 −1 4 7 1 3 2 −3 ]

ⓐ [ 11 9 −5 7 5 −1 ] [ 11 9 −5 7 5 −1 ] ⓑ [ 5 −3 2 −5 2 −1 −1 4 3 −2 2 −7 ] [ 5 −3 2 −5 2 −1 −1 4 3 −2 2 −7 ]

{ x − y + 2 z = 3 2 x + y − 2 z = 1 4 x − y + 2 z = 0 { x − y + 2 z = 3 2 x + y − 2 z = 1 4 x − y + 2 z = 0

{ x + y + z = 4 2 x + 3 y − z = 8 x + y − z = 3 { x + y + z = 4 2 x + 3 y − z = 8 x + y − z = 3

ⓐ [ −2 3 0 −2 4 −1 −4 4 5 −2 −2 −2 ] [ −2 3 0 −2 4 −1 −4 4 5 −2 −2 −2 ] ⓑ [ −2 3 0 −2 4 −1 −4 4 15 −6 −6 −6 ] [ −2 3 0 −2 4 −1 −4 4 15 −6 −6 −6 ] ⓒ [ −2 3 0 −2 3 4 −13 −16 −8 15 −6 −6 −6 ] [ −2 3 0 −2 3 4 −13 −16 −8 15 −6 −6 −6 ]

ⓐ [ 4 1 −3 2 2 −3 −2 −4 5 0 4 −1 ] [ 4 1 −3 2 2 −3 −2 −4 5 0 4 −1 ] ⓑ [ 8 2 −6 4 2 −3 −2 −4 5 0 4 −1 ] [ 8 2 −6 4 2 −3 −2 −4 5 0 4 −1 ] ⓒ [ 14 −7 −12 −8 2 −3 −2 −4 5 0 4 −1 ] [ 14 −7 −12 −8 2 −3 −2 −4 5 0 4 −1 ]

[ 1 −1 2 0 −3 −4 ] [ 1 −1 2 0 −3 −4 ]

[ 1 −1 3 0 −5 8 ] [ 1 −1 3 0 −5 8 ]

The solution is ( 4 , −1 ) . ( 4 , −1 ) .

The solution is ( −2 , 0 ) . ( −2 , 0 ) .

( 6 , −1 , −3 ) ( 6 , −1 , −3 )

( 5 , 7 , 4 ) ( 5 , 7 , 4 )

infinitely many solutions ( x , y , z ) , ( x , y , z ) , where x = z − 3 ; y = 3 ; z x = z − 3 ; y = 3 ; z is any real number.

infinitely many solutions ( x , y , z ) , ( x , y , z ) , where x = 5 z − 2 ; y = 4 z − 3 ; z x = 5 z − 2 ; y = 4 z − 3 ; z is any real number.

ⓐ −14 ; −14 ; ⓑ −28 −28

ⓐ 2 ⓑ −15 −15

ⓐ 3 ⓑ 11 ⓒ 2

ⓐ −3 −3 ⓑ 2 ⓒ 3

( − 15 7 , 24 7 ) ( − 15 7 , 24 7 )

( −2 , 0 ) ( −2 , 0 )

( −9 , 3 , −1 ) ( −9 , 3 , −1 )

( −6 , 3 , −2 ) ( −6 , 3 , −2 )

infinite solutions

The solution is the grey region.

No solution.

ⓐ { 30 m + 20 p ≤ 160 2 m + 3 p ≤ 15 { 30 m + 20 p ≤ 160 2 m + 3 p ≤ 15 ⓑ

ⓐ { a ≥ p + 5 a + 2 p ≤ 400 { a ≥ p + 5 a + 2 p ≤ 400 ⓑ

ⓐ { 0.75 d + 2 e ≤ 25 360 d + 110 e ≥ 1000 { 0.75 d + 2 e ≤ 25 360 d + 110 e ≥ 1000 ⓑ

ⓐ { 140 p + 125 j ≥ 1000 1.80 p + 1.25 j ≤ 12 { 140 p + 125 j ≥ 1000 1.80 p + 1.25 j ≤ 12 ⓑ

Section 4.1 Exercises

( 0 , 2 ) ( 0 , 2 )

( 2 , 4 ) ( 2 , 4 )

( −2 , 2 ) ( −2 , 2 )

( 3 , 3 ) ( 3 , 3 )

( 6 , −4 ) ( 6 , −4 )

No solutions, inconsistent, independent

1 point, consistent and independent

infinite solutions, consistent, dependent

( 1 , −4 ) ( 1 , −4 )

( −3 , 2 ) ( −3 , 2 )

( −1 / 2 , 5 / 2 ) ( −1 / 2 , 5 / 2 )

( −5 , 4 ) ( −5 , 4 )

( 0 , 10 ) ( 0 , 10 )

( 4 , −2 ) ( 4 , −2 )

( 4 , 0 ) ( 4 , 0 )

( 4 , 5 ) ( 4 , 5 )

( 7 , 12 ) ( 7 , 12 )

( −3 , −5 ) ( −3 , −5 )

( 2 , −3 ) ( 2 , −3 )

( −11 , 2 ) ( −11 , 2 )

( 6 / −9 , 24 / 7 ) ( 6 / −9 , 24 / 7 )

infinitely many

ⓐ substitution ⓑ elimination

ⓐ elimination ⓑ substituion

Answers will vary.

Section 4.2 Exercises

−7 −7 and −19 −19

22 and −67 −67

Eighty cable packages would need to be sold to make the total pay the same.

Mitchell would need to sell 120 stoves for the companies to be equal.

8 and 40 gallons

1000 calories playing basketball and 400 calories canoeing

Oranges cost $2 per pound and bananas cost $1 per pound

Package of paper $4, stapler $7

Hot dog 150 calories, cup of cottage cheese 220 calories

Owen will need 80 quarts of water and 20 quarts of concentrate to make 100 quarts of lemonade.

53.5 53.5 degrees and 36.5 36.5 degrees

16 degrees and 74 degrees

134 degrees and 46 degrees

37 degrees and 143 degrees

16 ° 16 ° and 74 ° 74 °

45 ° 45 ° and 45 ° 45 °

Width is 41 feet and length is 118 feet.

Width is 10 feet and length is 40 feet.

1.5 1.5 hour

Boat rate is 16 mph and current rate is 4 mph.

Boat rate is 18 mph and current rate is 2 mph.

Jet rate is 265 mph and wind speed is 22 mph.

Jet rate is 415 mph and wind speed is 25 mph.

Section 4.3 Exercises

110 adult tickets, 190 child tickets

6 good seats, 10 cheap seats

92 adult tickets, 220 children tickets

13 nickels, 3 dimes

42 dimes, 8 quarters

17 $10 bills, 37 $20 bills

80 pounds nuts and 40 pounds raisins

9 pounds of Chicory coffee, 3 pounds of Jamaican Blue Mountain coffee

10 bags of M&M’s, 15 bags of Reese’s Pieces

7.5 7.5 liters of each solution

80 liters of the 25% solution and 40 liters of the 10% solution

240 liters of the 90% solution and 120 liters of the 75% solution

$1600 at 8%, 960 at 6%

$28,000 at 9%, $36,000 at 5.5 % 5.5 %

$8500 CD, $1500 savings account

$55,000 on loan at 6% and $30,000 on loan at 4.5 % 4.5 %

ⓐ C ( x ) = 5 x + 6500 C ( x ) = 5 x + 6500

ⓑ R ( x ) = 10 x R ( x ) = 10 x

ⓓ 1,500; when 1,500 water bottles are sold, the cost and the revenue equal $15,000

Section 4.4 Exercises

( 4 , 5 , 2 ) ( 4 , 5 , 2 )

( 7 , 12 , −2 ) ( 7 , 12 , −2 )

( −3 , −5 , 4 ) ( −3 , −5 , 4 )

( 2 , −3 , −2 ) ( 2 , −3 , −2 )

( 6 , −9 , −3 ) ( 6 , −9 , −3 )

( 3 , −4 , −2 ) ( 3 , −4 , −2 )

( −3 , 2 , 3 ) ( −3 , 2 , 3 )

( −2 , 0 , −3 ) ( −2 , 0 , −3 )

x = 203 16 ; y = –25 16 ; z = –231 16 ; x = 203 16 ; y = –25 16 ; z = –231 16 ;

( x , y , z ) ( x , y , z ) where x = 5 z + 2 ; y = −3 z + 1 ; z x = 5 z + 2 ; y = −3 z + 1 ; z is any real number

( x , y , z ) ( x , y , z ) where x = 5 z − 2 ; y = 4 z − 3 ; z x = 5 z − 2 ; y = 4 z − 3 ; z is any real number

$20, $5, $10

Section 4.5 Exercises

ⓐ [ 2 4 −5 3 −2 2 ] [ 2 4 −5 3 −2 2 ] ⓑ [ 3 −2 −1 −2 −2 1 0 5 5 4 1 −1 ] [ 3 −2 −1 −2 −2 1 0 5 5 4 1 −1 ]

ⓐ [ 2 −5 −3 4 −3 −1 ] [ 2 −5 −3 4 −3 −1 ] ⓑ [ 4 3 −2 −3 −2 1 −3 4 −1 −4 5 −2 ] [ 4 3 −2 −3 −2 1 −3 4 −1 −4 5 −2 ]

{ 2 x − 4 y = −2 3 x − 3 y = −1 { 2 x − 4 y = −2 3 x − 3 y = −1

{ 2 x − 2 y = −1 2 y − z = 2 3 x − z = −2 { 2 x − 2 y = −1 2 y − z = 2 3 x − z = −2

ⓐ [ 3 2 1 4 −6 −3 ] [ 3 2 1 4 −6 −3 ] ⓑ [ 12 8 4 4 −6 −3 ] [ 12 8 4 4 −6 −3 ] ⓒ [ 12 8 4 24 −10 −5 ] [ 12 8 4 24 −10 −5 ]

ⓐ [ 2 1 −4 5 6 −5 2 3 3 −3 1 −1 ] [ 2 1 −4 5 6 −5 2 3 3 −3 1 −1 ] ⓑ [ 2 1 −4 5 6 −5 2 3 3 −3 1 −1 ] [ 2 1 −4 5 6 −5 2 3 3 −3 1 −1 ] ⓒ [ 2 1 −4 5 6 −5 2 3 −4 7 −6 7 ] [ 2 1 −4 5 6 −5 2 3 −4 7 −6 7 ]

[ 1 −2 3 −4 0 5 −11 17 0 1 −10 7 ] [ 1 −2 3 −4 0 5 −11 17 0 1 −10 7 ]

( 1 , −1 ) ( 1 , −1 )

( −2 , 5 , 2 ) ( −2 , 5 , 2 )

infinitely many solutions ( x , y , z ) ( x , y , z ) where x = 1 2 z + 4 ; y = 1 2 z − 6 ; z x = 1 2 z + 4 ; y = 1 2 z − 6 ; z is any real number

infinitely many solutions ( x , y , z ) ( x , y , z ) where x = 5 z + 2 ; y = −3 z + 1 ; z x = 5 z + 2 ; y = −3 z + 1 ; z is any real number

Section 4.6 Exercises

ⓐ 6 ⓑ −14 −14 ⓒ −6 −6

ⓐ 9 ⓑ −3 −3 ⓒ 8

( 7 , 6 ) ( 7 , 6 )

( −9 , 3 ) ( −9 , 3 )

inconsistent

Section 4.7 Exercises

ⓐ false ⓑ true

ⓐ { f ≥ 0 p ≥ 0 f + p ≤ 20 2 f + 5 p ≤ 50 { f ≥ 0 p ≥ 0 f + p ≤ 20 2 f + 5 p ≤ 50 ⓑ

ⓐ { c ≥ 0 a ≥ 0 c + a ≤ 24 a ≥ 3 c { c ≥ 0 a ≥ 0 c + a ≤ 24 a ≥ 3 c ⓑ

ⓐ { w ≥ 0 b ≥ 0 27 w + 16 b > 80 3.20 w + 1.75 b ≤ 10 { w ≥ 0 b ≥ 0 27 w + 16 b > 80 3.20 w + 1.75 b ≤ 10 ⓑ

ⓐ { w ≥ 0 r ≥ 0 w + r ≥ 4 270 w + 650 r ≥ 1500 { w ≥ 0 r ≥ 0 w + r ≥ 4 270 w + 650 r ≥ 1500 ⓑ

Review Exercises

( 3 , −1 ) ( 3 , −1 )

one solution, consistent system, independent equations

( 3 , 1 ) ( 3 , 1 )

( 4 , −1 ) ( 4 , −1 )

elimination

50 irises and 150 tulips

10 calories jogging and 10 calories cycling

35 ° 35 ° and 55 ° 55 °

the length is 450 feet, the width is 264 feet

1 2 1 2 an hour

the rate of the jet is 395 mph, the rate of the wind is 7 mph

41 dimes and 11 pennies

46 2 3 46 2 3 liters of 30% solution, 23 1 3 23 1 3 liters of 60% solution

$29,000 for the federal loan, $14,000 for the private loan

( −3 , 2 , −4 ) ( −3 , 2 , −4 )

[ 4 3 0 −2 1 −2 −3 7 2 −1 2 −6 ] [ 4 3 0 −2 1 −2 −3 7 2 −1 2 −6 ]

{ x − 3 z = −1 x − 2 y = −27 − y + 2 z = 3 { x − 3 z = −1 x − 2 y = −27 − y + 2 z = 3

ⓐ [ 1 −3 −2 4 4 −2 −3 −1 2 2 −1 −3 ] [ 1 −3 −2 4 4 −2 −3 −1 2 2 −1 −3 ] ⓑ [ 2 −6 −4 8 4 −2 −3 −1 2 2 −1 −3 ] [ 2 −6 −4 8 4 −2 −3 −1 2 2 −1 −3 ] ⓒ [ 2 −6 −4 8 4 −2 −3 −1 0 −6 −1 5 ] [ 2 −6 −4 8 4 −2 −3 −1 0 −6 −1 5 ]

( −2 , 5 , −2 ) ( −2 , 5 , −2 )

ⓐ { b ≥ 0 n ≥ 0 b + n ≤ 40 12 b + 18 n ≥ 500 { b ≥ 0 n ≥ 0 b + n ≤ 40 12 b + 18 n ≥ 500 ⓑ

Practice Test

( 2 , 1 ) ( 2 , 1 )

( 2 , −2 , 1 ) ( 2 , −2 , 1 )

15 liters of 1% solution, 5 liters of 5% solution

The candy cost $20; the cookies cost $5; and the popcorn cost $10.

ⓐ { C ≥ 0 L ≥ 0 C + 0.5 L ≤ 50 L ≥ 3 C { C ≥ 0 L ≥ 0 C + 0.5 L ≤ 50 L ≥ 3 C ⓑ

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Home > CCA > Chapter 4 > Lesson 4.2.3

Lesson 4.1.1, lesson 4.1.2, lesson 4.2.1, lesson 4.2.2, lesson 4.2.3, lesson 4.2.4, lesson 4.2.5, lesson 4.3.1.

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