Download Section 2.7

Section 2.7
Consecutive Integers
Consecutive integers are integers that are next to
each other on the number line
For example: 5 and 6
13 and 14
–4 and –3.
Consecutive odd integers are odd integers that
follow one another on the number line.
For example: 3 and 5
11 and 13
–9 and –7.
Translating words to algebraic statements.
The sum of two consecutive odd integers is 28.
Find the two integers.
Step 1: Understand:
Known items:
Numbers are integers
They are consecutive and odd
Adding them gives a total of 28.
Find: Both numbers
Step 2: Plan
Let x = the first consecutive odd integer
Always start with a
Let Statement
Then x + 2 is the next consecutive odd integer
x + (x + 2) = 28
Create an equation
Step 3: Carry Out
x + (x + 2) = 28
2x + 2 = 28
2x = 26
x = 13 and
(13) + 2 = 15
Simplify the left side
Add –2 to each side
Multiply each side by
Step 6: Check.
Suppose the first odd integer is 13.
The next consecutive odd integer is 15.
The sum of 15 and 13 is 28.
Answer:
13 and 15
Interest
You invest money in a bank account (or CD).
The account earns 8% in annual interest.
You invest the same amount plus an additional
$2,000 in a second account.
This account earns 9% in annual interest.
At the end of the year, the total interest earned in
both accounts is $690.
How much did you invest in each account?
Step 1: Understand
Known items:
The interest rates (8% and 9%)
The total interest earned ($690)
Investment at 9% is $2,000 more than investment
at 8%
Find:
The amount invested at 8%
The amount invested at 9%
Step 2: Plan
Let x = the amount of money invested at 8%.
Then, x + 2,000 = the amount of money invested at 9%.
The interest earned on x dollars invested at 8% is 0.08x.
The interest earned on (x + 2,000) dollars invested
at 9% is 0.09(x + 2,000).
Step 2: Plan
Let’s summarize this information in a table:
Because the total amount of interest earned from
both accounts is $690, the equation that describes
the situation is:
Interest earned + Interest earned = Total interest
at 8%
at 9%
earned
0.08x
+ 0.09(x + 2,000) =
690
Step 3: Carry Out
0.08x + 0.09(x + 2,000) = 690
0.08x + 0.09x + 180 = 690
0.17x + 180 = 690
0.17x = 510
Distributive property
Add 0.08x and 0.09x
Add –180 to each side
Divide each side by 0.17
x = 3,000 (at 8%)
and (3,000) + 2,000 = 5,000 (at 9%)
Step 4: Check
The interest at 8% is 8% of 3,000 or 0.08(3,000) = $240
The interest at 9% is 9% of 5,000 or 0.09(5,000) = $450
The total interest is $690
Triangles
One angle of a triangle is twice the smallest angle.
The other angle is three times as large as the
smallest angle.
Find the measure of all three angles.
Step 1: Understand
Known items:
The sum of the angles in a triangle is 180°
One angle is twice the smallest angle
The largest angle is three times the smallest angle.
Find: The measure of all three angles
Step 2: Plan
Draw a triangle
Label the smallest angle as x,
then 2x will be the measure of another angle and
3x will be the measure of the largest angle.
Step 2: Plan
Let Statement
Let x
= the measure of the smallest angle
Then, 2x = the measure of the second angle
and 3x = the measure of the third angle.
x + 2x + 3x = 180°
Equation
Step 3: Carry Out
x + 2x + 3x = 180°
6x = 180°
x = 30°
and 2(30°) = 60°
3(30°) = 90°
Step 4: Check.
The angles must add to 180°:
30° + 60° + 90° ≟ 180°
180° = 180°
Answer:
30°, 60°, 90°
Our answers check



Section 2.7
Page 179-184
# 1, 9, 15, 17, 21, 23
Please bring graph paper, a ruler and a pencil for
the next class.