Name: _____________________________________ Period: _____________ Date: ______________
Chapter #2:
Homework Packet #4
Day 1 – 4
COMPLETE THE FOLLOWING IN PENCIL ONLY. After completing the assignment, use the answer key
and a COLORED PEN to correct your work. Use your notes to help you answer the following. Answers are
provided.
#1 Consecutive Integers
Your answers to questions #1-3 are all related to solving the following problem.
Find three consecutive integers such that the sum of second and third is -43.
1. Which of the following is the correct let statements to solve this problem?
A. Let x = 1st consecutive integer, Let x + 2 = 2nd consecutive integer, Let x + 4= 3rd consecutive integer
B. Let x = 1st consecutive integer, Let x + 1 = 2nd consecutiveinteger, Let x + 2= 3rd consecutive integer
C. Let x + 1 = 1st consecutive integer, Let x + 3 = 2nd consecutiveinteger, Let x + 5= 3rd consecutive integer
D. Let x = 1st consecutive integer, Let x + 2 = 2nd consecutive integer, Let x + 3= 3rd consecutive integer
2. Which of the following is the correct equation to solve the problem above?
A. x + x + 1 + x + 2 = -43
B. x + x + 2 + x + 4 = -43
C. x + 2 + x + 3 = -43
D. x + 1 + x + 2 = -43
3. Using your answer from problem #2, what are the three consecutive integers? (HINT: Solve your equation.)
Show your work.
1
4. Find three consecutive integers such that the
sum of the first and third is 40.
5. Find three consecutive odd integers such that
the third is nine more than twice the sum of the
first and second.
MIXED REVIEW:
For each of the following: Find the value of A by substituting the other given values into the expression.
6. 𝐴 = 𝑠 2 when s = 5.5
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7. 𝐴 = 2 𝑏ℎ when b = 9.7 and h = 8.5
Solve each equation.
8. x + x + 1 = 95
9. 4n – (n + 2) = 2(n + 4 ) + 12
2
#2 Word Problems 1
For each question below write let statement(s) and an equation. Then answer the question by solving your
equation.
1. Eight times a number equals 35 more than the
number. Find the number.
3. One number is two less than the larger. If four
2. If twice a number is subtracted from 132, the result
equals four times the number. Find the number.
4. The greater of 2 numbers is 1 more than twice the
times the larger is subtracted from five times the
smaller. Three times the greater is ten more than 5
smaller, the result is 10. Find the numbers. (Hint:
times the smaller. Find the numbers.
you need two let statements)
(Hint: you need two let statements)
3
MIXED REVIEW:
Your answers to questions #5-7 are all related to solving the following problem:
Find three consecutive integers such that twice the smallest is 12 more than the largest.
5. Which of the following is the correct set of let
statements to solve this problem?
6. Which of the following is the correct equation to
solve the problem above?
A. x, 12 + x, x + 3
A. 2x = x + 3 + 12
B. x, x + 1, x + 2
B. x + 2 = x + 2 + 12
C. x, x + 1, x + 3
C. 2x = x + 2 + 12
D. x, x + 2, x + 4
D. 2x = x + 1 + 12
7. Using your answer from problem #6, what are the three consecutive integers? (HINT: Solve your equation.)
For each of the following: Find the value of A by substituting the other given values into the expression.
1
8. 𝐴 = 𝑏ℎ
2
when b = 3 and h = 6
9. 𝐴 = 𝑏ℎ
when b = 6.25 and h = 8.51
𝑏ℎ
10. 𝐴 =
2
when b = 10.4 and h = 13.6
4
#3 Word Problems 2
For each question below write let statement(s) and an equation. Then answer the question by solving your
equation.
1. The second of three numbers is 6 more than the first. The third number is twice the first. The sum of the
three numbers is 26. Find the three numbers.
2. The second of three numbers is 1 less than the first. The third number is 5 less than the second. If the first
number is twice as large as the third, find the three numbers.
3. Four times the lesser of two consecutive odd even integers is 4 more than twice the greater number. Find the
integers.
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MIXED REVIEW:
4. The ages of three brothers are consecutive integers
with the sum of 96. How old are the brothers?
5. The product of 16 and 4 less than a number is 208.
Find the number.
6. Solve |5 – 3x| = 32
7. Solve 0.25x + 0.05x = 0.90
8. Use the formula 𝐴 = 𝑏ℎ to find the area of the rectangle.
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#4 Perimeter Word Problems
1. If the lengths of the sides of a square are
represented by 3x - 1 then represent the perimeter
of the square as an expression.
2. The perimeter of a rectangular rugby field is 340
meters. If the length of the field is 30 meters less
than its width, what are the dimensions of the
rugby field?
3. The perimeter of a rectangle is 360 centimeters. If
the ratio of its length to its width is 11:4, find the
dimension of the rectangle.
4. The length and width of a rectangle are in the ratio
5:9. If the perimeter of the rectangle is 126, find
the dimensions of the rectangle.
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5. The larger side of a triangle is six more inches than the smallest side. The third side is twice the smallest
side. If the perimeter of the triangle is 30 inches, write and solve an equation to find the lengths of all three
sides of the triangle.
MIXED REVIEW:
Find the area of each polygon using the given formula and diagram.
6.
𝐴 = 𝑏ℎ
7.
𝐴=
𝑏ℎ
2
3
8. Solve |− 5 𝑥 − 7| = 14
9 mm
8
Answers
#1 Consecutive Integers
1) B
2) D
3) -23,-22,-21
4) 19,20,21
5) -3,-1,1
Mixed Review
6) 30.25
7) 41.225
8) 47
9) 22
#2 Word Problems 1
1) 5
2) 22
3) 18,20
4) 7,15
5) Mixed Review
6) B
7) C
8) 14,15,16
9) 9
10) 53.1875
11) 70.72
#3 Word Problems 2
1) 5,10,11
2) 6,11,12
3) 4,6
Mixed Review
4) 31, 32, 33
5) 17
37
6) {-9, 3 }
7) 3
8) 30.6 m2
#4 Perimeter Word Problems
1) 12x – 4
2) 70m by 100m
3) 48 cm by 132 cm
4) 22.5 by 40.5
5) 6 in, 12in, 12in
Mixed Review
6) 6.2 yd2
7) 3800 mm2
35
8) {-35, 3 }
Answers
#1 Consecutive Integers
1) B
2) D
3) -23,-22,-21
4) 19,20,21
5) -3,1,1
Mixed Review
6) 30.25
7) 41.225
8) 47
9) 22
#2 Word Problems 1
1) 5
2) 22
3) 18,20
4) 7,15
Mixed Review
5) B
6) C
7) 14,15,16
8) 9
9) 53.1875
10) 70.72
#3 Word Problems 2
1) 5,10,11
2) 6,11,12
3) 4,6
Mixed Review
4) 31, 32, 33
5) 17
37
6) {-9, 3 }
7) 3
8) 30.6 m2
#4 Perimeter Word Problems
1) 12x – 4
2) 70m by 100m
3) 48 cm by 132 cm
4) 22.5 by 40.5
5) 6 in, 12in, 12in
Mixed Review
6) 6.2 yd2
7) 3800 mm2
35
8) {-35, 3 }
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CONSECUTIVE INTEGERS
9. Find 3 consecutive integers such that the sum of the first and third equals -36.
10. Find four consecutive integers such that twice the second is 5 less than three times the fourth.
RATIO
1. Find the dimensions of a rectangle if the ratio of the length to the width is 3:4 and the perimeter is 28
cm.
EASIER PERIMETER
7. The length of a rectangle is 5 meters more than its width. The perimeter is 66 meters. Find the dimensions of
the rectangle.
8. The perimeter of a rectangle is 30 inches. If its length is three times its width, find the dimensions of the
rectangle.
9. The width of the rectangle is 3 yards less than its length. The perimeter is 130 yards. Find the length and the
width of the rectangle.
10. The length of a rectangle is triple its width. If the perimeter of the rectangle is 72 ft, find the dimensions of
the rectangle.
HARDER PERIMETER
1. The length of the second side of a triangle is 2 inches less than the length of the first side. The length of
the third side is 12 inches more than the length of the first side. The perimeter of the triangle is 73
inches. Find the length of each side of the triangle.
2. In a triangle, the measure of the second side is two less than twice the measure of the first side. The
measure of the third side is two more than the first side. If the perimeter of the triangle is 24 inches, find
the measure of each side of the triangle.
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