Practice the problems of Math in Focus Grade 6 Workbook Answer Key Chapter 8 Lesson 8.2 Writing Linear Equations to score better marks in the exam.

## Math in Focus Grade 6 Course 1 B Chapter 8 Lesson 8.2 Answer Key Writing Linear Equations

### Math in Focus Grade 6 Chapter 8 Lesson 8.2 Guided Practice Answer Key

**Complete.**

Question 1.

Isaiah has h baseball cards. Miguel has 7 more baseball cards than Isaiah.

a) Write an expression for the number of baseball cards that Miguel has in terms of h.

Miguel has baseball cards.

b) If Miguel has k baseball cards, express k in terms of h.

k = +

c) State the independent and dependent variables.

Independent variable: , dependent variable:

Answer:

a) Miguel has h + 7 baseball cards,

b) k = h + 7,

c) Independent variable: h, dependent variable: k,

Explanation:

Given Isaiah has h baseball cards. Miguel has 7 more baseball cards than Isaiah,

a) Wrote an expression for the number of baseball cards that Miguel has in terms of h as Miguel has h + 7 baseball cards.

b) If Miguel has k baseball cards expressing k in terms of h as k = h + 7.

c) The independent and dependent variables are independent variable is h and dependent variable are k which depends on value of h.

**Write an equation for each of the following. Then state the independent and dependent variables for each equation.**

Question 2.

Hannah took p minutes to jog around a park. Sofia took 12 minutes longer to jog around the park. If Sofia took t minutes to jog around the park, express t in terms of p.

Answer:

t = p + 12,

Independent variable : p, Dependent variable: t,

Explanation:

Given Hannah took p minutes to jog around a park. Sofia took 12 minutes longer to jog around the park. If Sofia took t minutes to jog around the park,To jog around the park it is p minutes, and Sofia took 12 more minutes if Sofia took t minutes expressing t in terms of p it is t = p + 12. Here p is independent variable and t is dependent variable on the value of p.

Question 3.

A bouquet of roses costs $30. A bouquet of tulips costs m dollars less. If the cost of one bouquet of tulips is n dollars, express n in terms of m.

Answer:

n = $30 – m,

Independent variable : m, Dependent variable: n,

Explanation:

Given a bouquet of roses costs $30. A bouquet of tulips costs m dollars less. If the cost of one bouquet of tulips is n dollars, expressing n in terms of m as n = $30 – m, Here m is independent variable and n is dependent variable on value of m.

Question 4.

Nathan has 7 boxes of marbles. Each box contains b marbles. If he has c marbles altogether, express c in terms of b.

Answer:

c = 7b,

Independent variable : b, Dependent variable: c,

Explanation:

Given Nathan has 7 boxes of marbles. Each box contains b marbles. If he has c marbles altogether, expressing c in terms of b as c = 7b as Nathan has 7 boxes of b marbles each here b is independent variable and c is dependent variable on the value of b.

Question 5.

A motel charges Mr. Kim x dollars for his stay. Mr. Kim stayed at the motel for 12 nights. If the rate per night for a room is y dollars, express y in terms of x.

Answer:

x = 12y,

Independent variable : b, Dependent variable: c,

Explanation:

Given a motel charges Mr. Kim x dollars for his stay. Mr. Kim stayed at the motel for 12 nights. If the rate per night for a room is y dollars expressing y in terms of x as it is x = 12y where y is independent variable and x is dependent variable on the value of y.

**Copy and complete the table. Then use the table to answer the questions.**

Question 6.

The width of a rectangular tank is 2 meters less than its length.

a) If the length is p meters and the width is q meters, write an equation relating p and q.

Answer:

Equation: q = p – 2,

Explanation:

Given The width of a rectangular tank is 2 meters less than its length.

a) If the length is p meters and the width is q meters so an equation relating p and q is q = p – 2,

If p =3 then q = 3 – 2 = 1,

If p = 4 then q = 4 – 2 = 2,

If p = 5 then q = 5 – 2 = 3,

If p = 7 then q = 7 – 2 = 5,

If p = 8 then q = 8 – 2 = 6,

Completed the table as shown above.

b) Use the data from a) to plot the points on a coordinate plane. Connect the points with a line.

Answer:

Explanation:

Used the data from a) to plot the points on a coordinate plane as length p meters on x – axis and width q meters on y axis. Connected the points with a line as shown above.

c) The point (5.5, 3.5) is on the line you drew in b). Does this point make sense in the situation?

Answer:

Yes,

Explanation:

The point(5.5,3.5) is on the line which i drew yes this point makes sense as p = 5.5 we have q = p – 2 = 5.5 – 2 = 3.5 which is true.

**Copy and complete each table. Then express the relationship between the two variables as an equation.**

Question 7.

Paul and Lee went to the library to borrow some books. Paul borrowed 6 more books than Lee.

Answer:

Equation: y = x + 6,

Explanation:

Given Paul and Lee went to the library to borrow some books. Paul borrowed 6 more books than Lee. If x is number of books Lee borrowed and y be books Paul borrowed so the equation is y = x + 6, so

if x = 1 then y = 1 + 6 = 7 books,

if x = 2 then y = 2 + 6 = 8 books,

if x = 3 then y = 3 + 6 = 9 books,

if x = 4 then y = 4 + 6 = 10 books and

if x = 5 then y = 5 + 6 = 11 books shown in the above table.

Question 8.

At a crafts store, Zoey bought some boxes of red beads and some boxes of blue beads. The number of boxes of red beads was 4 times the number of boxes of blue beads.

Answer:

Equation: r = 4b,

Explanation:

Given at a crafts store Zoey bought some boxes of red beads and some boxes of blue beads. The number of boxes of red beads was 4 times the number of boxes of blue beads. Let read beads be r and blue beads be b so the equation is r = 4b,

if b = 2 then r = 4 X 2 = 8 beads,

if b = 3 then r = 4 X 3 = 12 beads,

if b = 4 then r = 4 X 4 = 16 beads,

if b = 5 then r = 4 X 5 = 20 beads shown above in the table.

**Use the data in the table to plot points on a coordinate plane. Connect the points to form a line. Then write an equation to show the relationship between the variables.**

Question 9.

Answer:

Equation:

d = 50t,

Explanation:

Used the data in the table to plot points on a coordinate plane. Connected the points to form a line as shown above here d is the distance traveled in miles on y – axis and t is the time taken in t hours on x – axis. As distance traveled is increasing by 50 each hour an equation to show the relationship between the variables is d = 50t.

### Math in Focus Course 1B Practice 8.2 Answer Key

**Solve.**

Question 1.

Joshua is w years old. His brother is 3 years older than he is.

a) If his brother is x years old, express x in terms of w.

Answer:

x = w + 3,

Explanation:

Given Joshua is w years old. His brother is 3 years older than he is means brother is w + 3, So if his brother is x years old expressing x in terms of w as x = w + 3.

b) State the independent and dependent variables in the equation.

Answer:

Independent variable : w,

Dependent variable : x,

Explanation:

Here Joshua is w years old his brother is 3 years older than he is and if his brother is x years old then the independent variable is w and dependent variable is x on the value of w.

Question 2.

Rita has b markers. Sandy has 11 fewer markers than she has.

a) If Sandy has h markers, express h in terms of b.

Answer:

h = b – 11,

Explanation:

As Rita has b markers. Sandy has 11 fewer markers than she has means Sandy has b – 11 markers, If Sandy has h markers expressing h in terms of b as h = b – 11.

b) State the independent and dependent variables in the equation.

Answer:

Independent variable : b,

Dependent variable : h,

Explanation:

As Rita has b markers. Sandy has 11 fewer markers than she has means Independent variable is b and dependent variable is h on the value of b.

Question 3.

A small box of cereal weighs k grams. A jumbo box of cereal weighs 5 times as much.

a) If the weight of the jumbo box of cereal is m grams, express m in terms of k.

Answer:

m = 5k,

Explanation:

Given a small box of cereal weighs k grams. A jumbo box of cereal weighs 5 times as much means jumbo box is 5k, If the weight of the jumbo box of cereal is m grams, expressing m in terms of k as m = 5k.

b) State the independent and dependent variables in the equation.

Answer:

Independent variable : k,

Dependent variable : m,

Explanation:

As a small box of cereal weighs k grams and a jumbo box of cereal weighs 5 times as much here the independent variable is k and dependent variable is m on the value of k.

Question 4.

The area of Hank’s farm is n acres. The area of Hank’s farm is 8 times as large as the area of Stan’s farm.

a) If s represents the area of Stan’s farm, express s in terms of n.

Answer:

n = 8s,

Explanation:

Given the area of Hank’s farm is n acres. The area of Hank’s farm is 8 times as large as the area of Stan’s farm means Hank’s farm is 8 X Stan’s farm if s represents the area of Stan’s farm expressing s in terms of n is n = 8s.

b) State the independent and dependent variables in the equation.

Answer:

Independent variable : s,

Dependent variable : n,

Explanation:

Given the area of Hank’s farm is n acres. The area of Hank’s farm is 8 times as large as the area of Stan’s farm means Hank’s farm is 8 X Stan’s farm if s represents the area of Stan’s farm expressing s in terms of n here Independent variable is s and dependent variable is n which depends on s.

Question 5.

Ethan scored x points in a game. His younger sister scored 8 points when she played the same game. Their combined score was y points.

a) Write an equation relating x and y.

Answer:

y = x + 8,

Explanation:

Given Ethan scored x points in a game. His younger sister scored 8 points when she played the same game. Their combined score was y points. So an equation relating x and y is y = x + 8.

b) Copy and complete the table to show the relationship between x and y.

Answer:

Explanation:

Completed the table to show the relationship between x and y as y = x + 8,

if x = 10 then y = 10 + 8 = 18,

if x = 11 then y = 11 + 8 = 19,

if x = 12 then y = 12 + 8 = 20,

if x = 13 then y = 13 + 8 = 21,

if x = 14 then y = 14 + 8 = 22 and

if x = 15 then y = 15 + 8 = 23 as shown above.

Question 6.

There are x sparrows in a tree. There are 50 sparrows on the ground beneath the tree. Let y represent the total number of sparrows in the tree and on the ground.

a) Express y in terms of x.

Answer:

y = x + 50,

Explanation:

Given there are x sparrows in a tree. There are 50 sparrows on the ground beneath the tree. Let y represent the total number of sparrows in the tree and on the ground.So expressing y in terms of x is y = x + 50.

b) Make a table to show the relationship between y and x. Use values of x = 10, 20, 30, 40, and 50 in your table.

Answer:

Explanation:

Asked to make a table to show the relationship between y and x. Used values of x = 10, 20, 30, 40, and 50 in my table and completed as shown above in the equation y = x + 50,

When x = 10 then y = 10 + 50 = 60,

when x = 20 then y = 20 + 50 = 70,

when x = 30 then y = 30 + 50 = 80,

when x = 40 then y = 40 + 50 = 90,

when x = 50 then y = 50 + 50 = 100.

c) Graph the relationship between y and x in a coordinate plane.

Answer:

Explanation:

Graphed the relationship between y and x in a coordinate plane as shown above as sparrows x on x -axis and total number of sparrows y on y – axis.

Question 7.

A rectangle has a perimeter of P centimeters. Its width is b centimeters. Its length is double its width.

a) Express P in terms of b.

Answer:

P = 6b,

Explanation:

Given a rectangle has a perimeter of P centimeters. Its width is b centimeters. Its length is double its width.

So expressing P in terms of b as P = 2(2b + b). = 2(3b) = 6b.

b) Copy and complete the table to show the relationship between P and b.

Answer:

Explanation:

Given a rectangle has a perimeter of P centimeters. Its width is b centimeters. Its length is double its width.

So expressed P in terms of b as P = 6b completed the table to show the relationship between P and b above as

if b= 1 then P = 6 X 1 = 6,

if b = 2 then P = 6 X 2 = 12,

if b = 3 then P = 6 X 3 = 18,

if b= 4 then P = 6 X 4 = 24,

if b = 5 then P = 6 X 5 = 30 and

if b = 6 then P = 6 X 6 = 36.

Question 8.

Every month, Amaan spends 60% of what he earns and saves the rest. Amaan earns n dollars and saves r dollars each month.

a) Express r in terms of n.

Answer:

r = n – 0.6n,

Explanation:

Given every month, Amaan spends 60% of what he earns and saves the rest. Amaan earns n dollars and saves r dollars each month. Expressing r in terms of n as r = n – n X 60/100 = n – 0.6n.

b) Make a table to show the relationship between r and n. Use values of n = 100, 200, 400, and 500 in your table.

Answer:

Explanation:

Made a table above to show the relationship between r and n. Using values of n = 100, 200, 400, and 500 in my table and substituting in r = n – 0.6n as

if n = 100 then r = 100 – 0.6 X 100 = 100 – 60 = 40,

if n = 200 then r = 200 – 0.6 X 200 = 200 – 120 = 80,

if n = 300 then r = 300 – 0.6 X 300 = 300 – 180 = 120,

if n = 400 then r = 400 – 0.6 X 400 = 400 – 240 = 160 and

if n = 500 then r = 500 – 0.6 X 500 = 500 – 300 = 200.

c) Graph the relationship between n and r in a coordinate plane.

Answer:

Explanation:

Graphed the relationship between n and r in a coordinate plane as r = n – 0.6n where earnings n dollars on x – axis and savings r dollars on y – axis as shown above.

d) The point (287.5, 115) is on the line you drew in c). Does this point make sense in the situation? Explain.

Answer:

Yes,

Explanation:

Given the point (287.5, 115) is on the line I drew in c) checking in r = n – 0.6n, if n = 287.5 then r = 287.5 – 0.6 X 287.5 = 287.5 – 172.5 = 115 which matches so this point make sense in the situation.

Question 9.

The side length of a square is t inches. The perimeter of the square is z inches.

a) Express z in terms of t.

Answer:

z = 4t,

Explanation:

Given the side length of a square is t inches. The perimeter of the square is z inches. Expressing z in terms of t as perimeter of sqaure is 4 X side length so it is z = 4t.

b) Make a table to show the relationship between z and t. Use whole number values of t from 1 to 10.

Answer:

Explanation:

Made a table to show the relationship between z and t. Used whole number values of t from 1 to 10 in z – 4t as

if t = 1 then z = 4 X 1 = 4,

if t = 2 then z = 4 X 2 = 8,

if t = 3 then z = 4 X 3 = 12,

if t = 4 then z = 4 X 4 = 16,

if t = 5 then z = 4 X 5 = 20,

if t = 6 then z = 4 X 6 = 24,

if t = 7 then z = 4 X 7 = 28,

if t = 8 then z = 4 X 8 = 32,

if t = 9 then z = 4 X 9 = 36 and

if t = 10 then z = 4 X 10 = 40 shown above.

c) Graph the relationship between z and t in a coordinate plane.

Answer:

Explanation:

Graphed the relationship between z and t in a coordinate plane as the side length of a square is t inches on x – axis and the perimeter of the square is z inches on y – axis as shown above.

d) Use your graph to find the perimeter of the square when the length is 3.5 inches and 7.5 inches.

Answer:

1) 14 inches,

2) 30 inches,

Explanation:

Using my graph the perimeter of the square when the length is 3.5 inches is 4 X 3.5 = 14 inches and when the length is 7.5 inches the perimeter of the square is 4 X 7.5 inches = 30 inches respectively.