Download Challenge 11-1

Name
LESSON
Date
Class
Challenge
11-1 Consecutive Number Search
Consecutive numbers are numbers that come one after the other.
For example, 3 and 4 are consecutive whole numbers.
6 and 8 are consecutive even numbers.
7 and 9 are consecutive odd numbers.
If n a number, then n 1 is the next consecutive whole number
after n.
If n an even number, then n 2 is the next consecutive even
number after n.
If n an odd number, then n 2 is the next consecutive odd
number after n.
Solve. (Hint: Let n the first number. Then write an equation for
each sum.)
1. The sum of two consecutive numbers is 73. What are the
numbers?
2. The sum of two consecutive numbers is 131. What are the
numbers?
3. The sum of two consecutive even numbers is 70. What are the
numbers?
4. The sum of two consecutive even numbers is 158. What are the
numbers?
5. The sum of two consecutive odd numbers is 108. What are the
numbers?
6. The sum of two consecutive odd numbers is 180. What are the
numbers?
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All rights reserved.
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Holt Mathematics
Problem Solving
LESSON
11-1 Solving Two-Step Equations
Challenge
LESSON
11-1 Consecutive Number Search
Write the correct answer.
Consecutive numbers are numbers that come one after the other.
For example, 3 and 4 are consecutive whole numbers.
6 and 8 are consecutive even numbers.
7 and 9 are consecutive odd numbers.
1. Last week, Carlie had several rice
cakes and 3 granola bars as snacks.
The snacks contained a total of
800 calories. If each granola bar had
120 calories and each rice cake had
40 calories, how many rice cakes did
she have?
If n a number, then n 1 is the next consecutive whole number
after n.
If n an even number, then n 2 is the next consecutive even
number after n.
11 rice cakes
If n an odd number, then n 2 is the next consecutive odd
number after n.
1. The sum of two consecutive numbers is 73. What are the
numbers?
n (n 1) 73; 36 and 37
2. The sum of two consecutive numbers is 131. What are the
numbers?
Activity
5. Kamisha swims for 0.25 hour. How
many calories does she burn?
A 30 calories
C 1.95 calories
B 195 calories
D 117 calories
4. The sum of two consecutive even numbers is 158. What are the
numbers?
n (n 2) 158; 78 and 80
Calories (per min)
Basketball
7.5
Cycling (10 mi/h)
5.5
Jogging
9.3
Swimming
7.8
6. Stu jogs at a rate of 5 mi/h. How far
must he jog to burn 418.5 calories?
F 9 mi
H 3.75 mi
G 4.65 mi
J 45 mi
5. The sum of two consecutive odd numbers is 108. What are the
numbers?
n (n 2) 108; 53 and 55
6. The sum of two consecutive odd numbers is 180. What are the
numbers?
8. How many hours would you have
to ride your bike at 10 mi/h to burn
550 calories?
H 1.0 hr
F
1.67 hr
G 1.5 hr
J 0.75 hr
7. Terry rides her bike for 40 minutes
and plays basketball for an hour. How
many calories does she burn?
A 67 calories
C 670 calories
B 560 calories
D 1,300 calories
n (n 2) 180; 89 and 91
9
Calories Used in Activities
The table shows calories burned by a
person performing different activities.
n (n 2) 70; 34 and 36
Holt Mathematics
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Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Reading Strategies
LESSON
11-1 Follow a Procedure
Holt Mathematics
Puzzles, Twisters & Teasers
LESSON
11-1 Sun, Sand, and Snakes!
To solve two-step equations, follow these steps.
Solve each equation. Then use the letters of the variables
to answer the riddle.
To Solve Two-Step Equations
3n 5 23
3n 5 5 23 5
3n 18
Step 3: Compute and
simplify the solution.
4 servings
Choose the letter for the best answer.
3. The sum of two consecutive even numbers is 70. What are the
numbers?
Step 2: Get the variable
by itself. Use the inverse
operation.
4. Brandon follows a 2,800 calorieper-day diet. He has 11 servings of
breads and cereals, which average
140 calories each. Yesterday, he had
a combined 9 servings of fruits and
vegetables, averaging 60 calories
each. How many 180-calorie servings
of meat and milk did he have to
complete his diet?
50 calories
n (n 1) 131; 65 and 66
Step 1: Get the variable
term by itself. Use the
inverse operation.
lunch
3. Erika is following a 2,200 calorieper-day diet. She eats the
recommended 9 servings of breads
and cereals, averaging 120 calories
per serving. She also eats 5 servings
of vegetables. If the rest of her daily
intake is 870 calories, what is the
average number of calories in each
serving of vegetables?
Solve. (Hint: Let n the first number. Then write an equation for
each sum.)
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
2. Jo eats 2,200 calories per day. She
eats 450 calories at breakfast and
twice as many at lunch. If she eats
three meals with no snacks, which
meal will contain the most calories?
3n
18
3
3
Subtract 5 from both
sides.
Divide both sides by 3.
s
1. 6 21 28
s 42
2. 4n 7 17
n 6
3. 6a 4 10
a 1
4. i 10 6
i 12
5. 7t 8 27
3
t 5
c
6. 8 25 20
c 40
7. 9e 15 93
e 12
8. 3o 8 35
o 9
9. 5r 13 15
r 2
5
10. 6m 4 22
m 3
n6
Answer the following questions.
1. What is the first step in solving a two-step equation?
Use the opposite operation to get the term with a variable by itself.
2. Which term in the equation above does not contain a variable?
5
What kind of shoes do snakes wear to the beach?
3. What operation was performed to remove that term?
W
5 was subtracted from both sides of the equation
A
1
T
5
E
R
M
O
12
2
5
3
9
C
C
40 40
A
S
I
N
S
1
42
12
6
42
4. What is the second step in solving a two-step equation?
Get the variable by itself.
5. Which term in the equation contains a variable?
3n
6. What operation was performed to get the n by itself?
division
7. What is the third step in a two-step equation?
Compute and simplify.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
11
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Holt Mathematics
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
90
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Holt Mathematics
Holt Mathematics