Wkst 2-A
Class Notes Writing Equations
Algebra 1CP
Translate the sentence into an equation.
Three
times a number is 36.

3n
= 36
Example 1 Translate each sentence into an equation.
a. Four times n is the difference of 30 and n.
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b. Nine increased by a number is five squared.
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c. Ten less than a number is fifty.
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d. The sum of two and a number is 9.
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e. A number decreased by five is four squared plus six.
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f. The sum of a number and six, divided by three is eight.
____________________________________________
Example 2 Translate each sentence into an equation.
a. Fifteen more than z times 6 is y times 2 minus eleven.
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b. Seven increased by a number is 21.
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c. A number b divided by three is six less than c.
____________________________________________
d. Twenty-seven times k is h squared decreased by 9.
____________________________________________
e. Nine times a number subtracted from 95 equals 37.
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f. Two plus the quotient of a number and 8 is 16.
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Wkst 2-B Class Notes (Power Point) A Problem Solving Plan
Alg 1CP
Verbal models are made up of
Algebraic models are made up of
Example 1: In a game, Ben’s score was 3 times Sam’s score. Together they scored 80 points.
Find their scores.
Assign Labels
Verbal Model
Algebraic Model
Example 2: Meg’s age is 5 times Jose’s age. The sum of their ages is 18. How old is each?
Assign Labels
Verbal Model
Algebraic Model
Example 3: A ribbon 24 feet long is cut into two pieces. The longer piece is four feet longer
than the shorter piece. What are the lengths of the pieces?
Assign Labels
Verbal Model
Algebraic Model
Example 4: Together Gini and JoAnn own 87 pairs of shoes. JoAnn has 25 more pairs than
Gini has. How many pairs does Gini have?
Assign Labels
Verbal Model
Algebraic Model
Wkst 2-C “Consecutive Integers”
Alg 1CP
Consecutive integers: Increase by one; Starting with 5, the next four
consecutive integers are 6, 7, 8, and 9.
Ex. A: Two consecutive integers have a sum of 77. Find the integers.
1) Variable
Let n = the first integer
Let n + 1 = the second integer
(by definition of the word consecutive the numbers must be one apart)
2) Words
3) Equation
4) Solve
5) Solution:
first integer + second integer = sum
n   n  1  77
2n 1  77
2n  1  1  77  1
4.)
Find three consecutive integers such that sum of
the first and third is 22.
5.)
The numbers are 38 and 39.
Let n = the first odd integer
Let n + 2 = the second odd integer
first odd
integer + second odd integer = sum
3) Equation
n   n  2  92
4) Solve
2n  2  92
2n  2  2  92  2
2n  90
2n 90

2
2
n  45
5) Solution:
2.) The sum of three consecutive integers is 234. What
are the numbers?
3.) Find two consecutive odd integers whose sum is -68.
2n 76

2
2
n  38
(even or odd consecutive integers would always be two apart ex: 3, 5, 7 or 2, 4,
6.)
2) Words
1.) The sum of two consecutive integers is 243. What
are the two integers?
2n  76
Ex. B (Even or Odd): Two consecutive odd integers have a sum of 92.
Find the integers.
1) Variable
Practice:
The numbers are 45 and 47.
Find three consecutive odd integers whose sum is
243.
6.) The sum of two consecutive integers is 345. What
are the two integers?
7.) The sum of two numbers is 151. The second number
is one more than twice the first number. What are the
two numbers?
8.) There are three numbers. The first is twice as big
as the second, and the second is twice as big as the
third. The total of the numbers is 161. What is the
smallest of the numbers?
9.)
The sum of two consecutive odd integers is 172.
What are the two integers?
10.) The sum of two consecutive even integers is 446.
What are the two integers?
Wkst 2-D
DISTANCE Opposite Directions
Alg 1CP
D1  D2  Total Distance
Ex. A: Two trains left the same station at the same time and traveled in opposite
directions. The E train averaged 130 km/h. The A train’s speed was 110 km/h. In
how many hours were they 480 km apart?
Starting point
E Train
A Train
480 km
1. Assign Labels. let t = time (until they are 480 km apart)
2. Verbal Model.
3. Algebraic Model.
E train’s distance
A train’s
total
and A train’s
distance + distance = distance
distance is
d1
+
d2
= 480
unknown. Since d
 480
= rt substitute rt
 480
for d.
E train’s
rt
Substitute rt for d
Substitute given values.130t
Solve.

rt
 110t
240t
t
4. Sentence.
 480
 2
The trains were 480 km apart in two hours.
Ex. B: Two cars traveled in opposite directions from the same starting point. The rate of
one car was 20 km/h less than the rate of the other car. After 5 hours, the cars were 700
km apart. Find the rate of each car.
Practice:
1) Two trucks started toward each other at the same time from towns 270 km apart. One
truck averaged 70km/h, and the other averaged 65 km/h. After how many hours did they
pass each other?
2) Two cars traveled in opposite directions from the same starting point. The rate of one car
was 10 km/h faster than the rate of the other car. After 4 hours the cars were 460 km
apart. Find each car’s rate.
3) Two motor homes traveled in opposite directions from the same starting point. The rate
of one motor home was 10 km/h less than the rate of the other motor home. After 10 hours,
the motor homes were 500 km apart. Find the rate of each motor home.
Wkst 2-E (Homework) Distance Problems
Algebra 1 CP
1) Two cars started toward each other at the same time from towns 330 km apart. One car
averaged 45 km/h, and the other averaged 65 km/h. After how many hours did they pass
each other?
2) Two trucks traveled in opposite directions from the same starting point. The rate of one
car was 12 km/h faster than the rate of the other car. After 5 hours the cars were 420 km
apart. Find each car’s rate.
3) Two motor homes traveled in opposite directions from the same starting point. The rate
of one motor home was 15 km/h less than the rate of the other motor home. After 8 hours,
the motor homes were 600 km apart. Find the rate of each motor home.
4) Two cars traveled in opposite directions from the same starting point. The rate of one car
was 20 km/h less than the rate of the other car. After 6 hours, the cars were 660 km apart.
Find the rate of each car.
5) Two trucks started toward each other at the same time from cities 368 km apart. One
truck averaged 50km/h, and the other averaged 42 km/h. After how many hours did they
pass each other?
6) Two cars traveled in opposite directions from the same starting point. The rate of one car
was 10 km/h faster than the rate of the other car. After 3 hours the cars were 360 km
apart. Find each car’s rate.
7) Two trucks traveled in opposite directions from the same starting point. The rate of one
truck was 20 km/h more than the rate of the other truck. After 10 hours, the motor homes
were 700 km apart. Find the rate of each truck.
8) Two cars started toward each other at the same time from towns 560 km apart. One
truck averaged 45 km/h, and the other averaged 35 km/h. After how many hours did they
pass each other?
HW Wkst 2-E KEY
1.
2.
3.
4.
5.
6.
7.
8.
3 hours
36 km/h and 48 km/h
45 km/h and 30 km/h
65 km/h and 45 km/h
4 hours
55 km/h and 65 km/h
25 km/h and 45 km/h
7 hours
Wkst. 2F # Theory and Travel Class Work
Alg.1CP
Example 1: The sum of the ages of two sisters is 25. The second sister’s age is 5 more
than three times the first sister’s age. Find the two ages.
Variable
Words
Equation
Solve
Solution
Example 2: A carpenter cuts a board that is 10 feet long into two pieces. The longer
piece is two feet longer than three times the length of the shorter piece. What is the
length of each piece?
Example 3: There are three numbers. The first is twice as big as the second, and the
second is twice as big as the third. The total of the numbers is 224. What is the
smallest of the numbers?
Example 4: Mary and Betty have saved $43 all together. Betty has saved $3 more than
3 times the amount Mary has saved. How much money has each girl saved?
Example 5: Marge worked 3 times as many problems as Sue. They worked a total of 32
problems. How many problems did Sue work?
Example 6: Joe and Janna leave home at the same time, traveling in opposite directions.
Joe drives 45 miles per hour and Janna drives 40 miles per hour. In how many hours will
they be 510 miles apart?
Example 7: Two trains leave the station at the same time, one traveling north, and the
other south. The first train travels at 50 miles per hour and the second at 60 miles per
hour. In How many hours will the trains be 275 miles apart?