## Everyday Mathematics 6th Grade Answer Key Unit 8 Applications: Ratios, Expressions, and Equations

### Everyday Mathematics Grade 6 Home Link 8.1 Answers

**Increasing Yield per Square Foot**

The diagram below shows the layout of a garden that has both rows and squares.

Use the yields on the diagram and the table information to determine which plant is in each row or square foot.

Question 1.

Label each garden bed to show what kind of plant and how many of the plants fill the row or square foot.

Answer:

Question 2.

a. What is the total expected yield for the garden in Problem 1? ____________

b. What is ? ____________

Answer:

a. The total expected yield for the garden in problem 1 is 68.5 pounds

b. The overall rate of plants per square foot is about 2/3 plant to 1 ft ^{2}

Question 3.

a. About how much more should the garden yield if beds I and II are changed from row garden beds to square-foot garden beds? (Assume the same plant would still be planted in each.) ____________

b. What would the overall rate of plants per square foot be? ____________

Answer:

a. About 2 more pounds should the garden yield if beds I and II are changed from row garden beds to square-foot garden beds.

b. The overall rate of plants per square foot is is 1 plant to 1 ft ^{2}

**Practice**

Solve the equations.

Question 4.

\(\frac{1}{2}\)p = 87; p = ________

Answer:

174

Explanation :

1/2 x p = 87

p = 87 x 2 = 174

Therefore, the value of p is 174

Question 5.

\(\frac{2}{3}\)d = 56; d = __________

Answer:

84

Explanation :

2/3 x d = 56

d = 56 x 3 / 2

d = 28 x 3 = 84

Therefore, the value of d is 84

Question 6.

\(\frac{7}{8}\)k = 84; k = __________

Answer:

96

Explanation :

7/8 x k = 84

k = 84 x 8 /7

K = 12 x 8 = 96

Therefore, the value of k is 96

### Everyday Math Grade 6 Home Link 8.2 Answer Key

Question 1.

Using Scale Drawings Julian made a scale drawing of his bedroom wall. He has artwork that he and his brother made hanging on the wall. His wall is 7 feet high and 12 feet long.

a. What scale did he use? ________

b. Use his scale drawing to complete the table.

Answer:

a. The scale he used is 1/2 inch equals to 1 foot ( 1/2 inch = 1 foot )

b.

Question 2.

Explain how you found the actual dimensions for Artwork B.

_______________________

______________________

Answer:

2 Squares = 1 foot

4 Squares = 2 feet

So, 5 squares = 25 Feet

Question 3.

Why might someone make a scale drawing of a planned artwork arrangement?

_______________________

________________________

Answer:

To make sure that result is so perfect and so accurate.

**Practice Solve.**

Question 4.

15% of x is 6. 100% of x is ________

Answer:

40

Explanation :

15 % = 15/100

Given,

15% of x is 6

= 15/100 X x -= 6

x = 100 X 6 /15

x = 40

And 100% = 100/100 = 1

Therefore, 100% of 40 is 1 x 40 = 40.

Question 5.

90% of y is 18. 100% of y is ________.

Answer:

20

Explanation:

90% = 90/100

Given,

90% of y is 18

= 90/100 X y = 18

y = 18 X 100 /90

y = 20

And 100% = 100/100 = 1

Therefore, 100% of 20 is 1 X 20 =20

### Everyday Mathematics Grade 6 Home Link 8.3 Answers

**Stretching Triangles**

Question 1.

Plot the original ordered pairs from the table in Problem 2, and connect points to make triangle ABC and triangle ADE.

Answer:

Question 2.

If you want to make triangle ABC and triangle ADE twice as tall and twice as wide, what would the new coordinates be? Write them in the table below.

Answer:

Question 3.

What is the distance from D to E in the enlarged figure? ________

Answer:

The distance from D to E in the enlarged figure is 4 units

Question 4.

What is the distance from D to E in the original figure? __________

Answer:

The distance from D to E in the original figure is 2 Units

Question 5.

Use ratio notation to represent the ratio of side length \(\ over line{D E}\) in the enlarged figure to side length \(\over line{D E}\) in the original figure. _______

Answer:

2 :1

**Practice Solve.**

Question 6.

\(\frac{3}{4}\) (4 – \(\frac{2}{3}\)) = _______

Answer:

3/4 X [4-2/3]

3/4 X[ 10/3]

= 5/2

Question 7.

3 + \(\frac{1}{2}\) ÷ 3 = ________

Answer:

3 + [ 1/2 / 3]

3 + [1/6]

= 19/6

Question 8.

______ = 2\(\frac{1}{2}\) ÷ (\(\frac{4}{3}\) – \(\frac{1}{2}\))

Answer:

[5/2] / (4/3-1/2)

[5/2] / ( 5/6)

= 3

### Everyday Math Grade 6 Home Link 8.4 Answer Key

**Modeling Distances in the Solar System**

Today the class made scale models of celestial bodies.

Imagine you are modeling the distance of each planet from the Sun.

Question 1.

Calculate the distance from the Sun in your model using the scale given in the table. Complete the table.

Answer:

Question 2.

Would this scale work for building the model in your classroom? Why or why not?

_____________________________

______________________________

Answer:

No, this scale not work for building the model in our classroom. Because, this scale is too large for the distances.

Question 3.

What scale for distance might work for a model in your classroom?

___________________________________

Answer:

The scale for distance might work for a model in our classroom is

1 cm = 10 million kilometres

Practice

Solve.

Question 4.

\(\frac{t}{12}\) = 8 ______

Answer:

t/12 =8

t = 8 X 12

Therefore, t = 96

Question 5.

p ÷ 9 = 11 _______

Answer:

p/9 =11

p= 99

Question 6.

n + 0.35 = 5 ________

Answer:

n+0.35 = 5

n = 4.65

### Everyday Mathematics Grade 6 Home Link 8.5 Answers

**Comparing Player Density**

The dimensions of the playing surfaces for four sports are listed below.

Football: 360 ft by 160 ft

Hockey: 200 ft by 85 ft (Ignore round corners)

Basketball: 50 ft by 94 ft

Baseball: 108,500 ft2 (Average for major league parks)

During a game, there are 22 players on a football field, 10 on a basketball court, 10 on a baseball diamond (not counting base runners), and 12 on an ice hockey rink. Calculate the square feet of playing area per player for each sport.

Question 1.

Football playing area: ___________

Area per player: ____________

Answer:

Football playing area is 57,600 Square feet

Area per player is 2618 Square feet

Question 2.

Basketball playing area: ____________

Area per player: ____________

Answer:

Basketball playing area is 4700 Square feet

Area per player is 470 Square feet

Question 3.

Hockey playing area: ____________

Area per player: ____________

Answer:

Hockey playing area is 17,000 Square feet

Area per player is 1417 Square feet

Question 4.

Baseball playing area: ____________

Area per player: ____________

Answer:

Baseball playing area is 108,500 Square feet

Area per player is 10,850 Square feet

Question 5.

a. Which sport is the most “crowded”? ____________

b. Justify your answer. ____________

Answer:

a. Basket ball is the sport is most crowded

b. Number of players are same as other sports even though Basketball has the smallest area. Hence, Basketball is most crowded.

Question 6.

Describe the relationship between square feet per player and player density.

__________________________

Answer:

The relationship between square feet per player and player density is “the number of square feet per player is directly proportional to spread of the player ” means the larger the number of square feet per player, the more spread of the players.

Question 7.

If the player density is lower, how might that affect their role in the game?

___________________________

Answer:

The team in which the player density is low , then it’ll be in a chance of losing side. Hence, it is the responsibility of each player to cover more of the playing the field.

**Practice Simplify the expressions.**

Question 8.

7t – 4t ________

Answer:

7t-4t = 3t

Question 9.

5 + 7r – 1.5 – 2r _______

Answer:

5 + 7r – 1.5 – 2r

(5-1.5) +(7r-2r)

3.5+5r

Question 10.

9(3c) ______

Answer:

27c

Question 11.

\(\frac{1}{2}\) (4b + 12) _______

Answer:

1/2 (4b/12)

(4b/2)/(12/2)

2b/6.

### Everyday Math Grade 6 Home Link 8.6 Answer Key

**Mobiles**

The mobiles shown in Problems 1 and 2 are in balance.

All measures are in feet for distances or pounds for weight.

Question 1.

What is the weight of the object on the left of the fulcrum?

W = __________

D = _________

w = _________

d = _________

Equation: _________

Solution: _________

Weight: _________

Answer:

W = 3x

D = 8

w = 15

d = 8

Equation : (3x)8 =(15)8

Solution: x = 15 ,5

Weight:

Question 2.

What is the distance of each object from the fulcrum?

W = _________

D = _________

w = _________

d = _________

Equation: _________

Solution: _________

Distance on the left of the fulcrum: _________

Distance on the right of the fulcrum: _________

Answer:

W = 8

D = x+4

w = 16

d = x-4

Equation: 8(x+4) = 16(x-4)

Solution: x=12

Distance on the left of the fulcrum: 16 lb

Distance on the right of the fulcrum: 8 lb

Question 3.

a. Sketch a mobile that will balance.

Label all lengths and weights.

Answer:

b. Use the mobile formula to explain why your mobile balances.

Answer:

**Practice**

Divide.

Question 4.

34.5 ÷ 0.5 = ______

Answer:

69

Question 5.

8.46 ÷ 4.7 = _______

1.8

Answer:

Question 6.

______ = 1.22 ÷ 4

Answer:

0.305

Question 7.

______ = 26.88 ÷ 0.48

Answer:

56

### Everyday Mathematics Grade 6 Home Link 8.7 Answers

**Generalizing Patterns**

Question 1.

Use the pattern pictured below. Shade a constant part of the pattern.

a. In the table, record numeric expressions for the total number of squares that represent what is shaded and how the pattern is growing.

Plan your numeric expressions to show one part of the expression as constant and the other part as varying.

b. Write an algebraic expression for the number of squares in Step n.

Answer:

a.

b.

an algebraic expression for the number of squares in Step ‘n’ is 5+2(n-1)

Question 2.

Circle an expression for finding the number of squares needed to build Step n that best represents how the pattern is shaded.

3 + 2n + n + 1

4 + 3n

6 + n + 2(n – 1)

7 + 3(n – 1)

Answer:

3+2n+n+1

Question 3.

Explain why the expression you chose in Problem 2 is the best match.

Answer:

The expression 3+2n+n+1 is best match because it is showing the third (3rd) row is shaded and also showing that multiple of 2 is added on top and also the number added at the bottom also the same number shaded at bottom.

Practice Simplify.

Question 4.

5(x + 10) = ______

Answer:

5x+50

Question 5.

2(x + 8) = _______

Answer:

2x+16

Question 6.

6x + 2x = _____

Answer:

8x

### Everyday Math Grade 6 Home Link 8.8 Answer Key

**Using Anthropometry**

The following passage is from Gulliver’s Travels by Jonathan Swift. The setting is Lilliput, a country where the people are only 6 inches tall. “Two hundred seamstresses were employed to make me shirts . . . . The seamstresses took my measure as I lay on the ground, one standing at my neck, and another at my mid leg, with a strong cord extended, that each held by the end, while the third measured the length of the cord with a rule of an inch long. Then they measured my right thumb and desired no more; for by a mathematical computation, that twice round the thumb is once round the wrist, and so on to the neck and the waist, and by the help of my old shirt, which I displayed on the ground before them for a pattern, they fitted me exactly.”

Question 1.

Four body parts are referenced in the text. What are they?

Choose a variable to represent each one.

Answer:

Four body parts are Neck (N) , Leg (L) , Thumb(T) , Waist(W)

Question 2.

Take these four measures on yourself, measuring to the nearest \(\frac{1}{4}\) inch.

Answer:

The four measurements are 1/4, 2/4, 3/4, 4/4.

Question 3.

Use the variables you recorded in Problem 1 to write three rules described in the text.

Answer:

The three rules are W=2T ; N=2W ; L=2N

Question 4.

Based on your data, how well do you think Gulliver’s new clothes fit? Explain.

Answer:

Being the measurements are by a mathematical computation, the measurements are accurately and fit exactly for Gulliver.

Practice

Evaluate.

Question 5.

5 \(\frac{1}{2}\) ÷ \(\frac{1}{4}\) = ________

Answer:

22

Question 6.

______ = 2 \(\frac{2}{3}\) ÷ \(\frac{3}{4}\)

Answer:

32/9

### Everyday Mathematics Grade 6 Home Link 8.9 Answers

Which Would You Rather Have ?

Don’s boss is offering him two choices to get paid for June.

- Choice #1 is to receive $10 on June 1st, $20 on June 2nd, $30 on June 3rd, and so on through June 30th.
- Choice #2 is to receive 1 penny the first day, 2¢ the second day, 4¢ the third day, and so on, doubling the amount each day for the rest of the month.

Question 1.

a. Predict which is the better plan. _________

b. Explain how you made your choice. ___________

Answer:

a.

Choice 1

b.

Because, at the end of the month, total will be higher in first case when compared to second case

Question 2.

Enter formulas to complete the table for the first five days of each plan.

Answer:

for choice 1 : 10x

for second case : (0.01)(2^(x-1))

Question 3.

Use a spreadsheet program or a calculator to determine how much Don would receive for the day on June 30th for each choice.

Choice 1: _________

Choice 2: _________

Answer:

Choice 1: $300

Choice 2: 5,368,709.12

Question 4.

If you have a spreadsheet program, find the total amount Don receives for both choices. If you do not, explain how to find the totals on the back of this page

Choice 1: _________

Choice 2: ________

Answer:

Choice 1: $4,650

Choice 2: $10,737,418.23

**Practice**

Write three equivalent ratios for each ratio.

Question 5.

2.5 to 2 ______

Answer:

1.25:1 , 5:4 , 10:8

Question 6.

1 : 1.4 ________

Answer:

2:2.8 , 20:28 , 40:56

Question 7.

\(\frac{1}{2}\) to 3 _______

Answer:

1:6 , 2:12 , 5:30

Question 8.

\(\frac{1}{2}\) : \(\frac{3}{4}\) _______

Answer:

1:1.5 , 2:3 , 4:6