Transcript Using_Equations

Algebra 2
2.2
Pinkston
SAT Question
If
A.
B.
C.
D.
E.
16  2k,
1
2
3
4
8
what is the value of k?
16  4  2
2
Review of words to translate English into
algebra:
Addition: sum, total, increased by, more
than, plus, longer than
Subtraction: difference, decreased by, less
than, subtracted from, minus; fewer than,
less (Those in italics and blue switch the
order from English to algebra).
Multiplication: product, times, twice, of,
double, triple
Division: quotient, over, divided by, ratio
Equality: is, the result is, equals, is the
same as
Don’t confuse less
than (subtraction)
with is less than (<)
x
Translate:
1. The ratio of a number and 4. 4 2
x
2. Two-thirds of a number.
3
3. The difference between 5 and a
number.
5 x
4. The sum of a number and 3. x  3
Ten fewer than a number. x 10
The product of a number and 3. 3x
A number decreased by 15. x 15
Three times the sum of a number
and 6. 3( x  6)
9. The sum of the quantity three times
a number and 6. 3x  6
x y
10. The average of x and y.
5.
6.
7.
8.
2
11. Thirty percent of a number. 0.3x
Solving Word Problems
1.
Heading
_________________________________
2.
Equation
_________________________________
3.
Solve
_________________________________
4.
Solution
_________________________________
Example 1: A 28-ft rope is cut into two
pieces. One piece is 3 ft longer than the
other. How long are the pieces?
Heading: first piece  x
other piece  3  x
Equation:
(Solve)
Solution:
x  3  x  28
2x  3  28
2x  25
x  12.5
12.5 ft and 15.5 ft
Example 2: A 23-ft cable is cut into two
pieces, one three times as long as the
other. How long are the pieces?
first piece  x
Heading:
other piece  3x
Equation:
(Solve)
Solution:
x  3x  23
4x  23
x  5.75
3x  17.25
5.75 ft and 17.25 ft
Example 3: Five plus twice a number is
seven times the number. What is the
number?
Heading: the number  x
Equation:
(Solve)
Solution:
5  2x  7 x
5  5x
1 x
1
Example 4: If seven times a certain
number is subtracted from 6, the result is
five times the number. What is the
number?
Heading: the number  x
Equation:
(Solve)
Solution:
6  7 x  5x
6  12x
1
x
1
2
2
Example 5:
Chris bought a baseball card in 1975.
By 1985, the value of the card had tripled. Since
1985, the value has increased by another $30. The
card is now worth 5 times its original value. How
much was the card worth when Chris bought it?
Heading: original value  x
value in 1985  3x
value now  3 x  30
Equation:
(Solve)
Solution:
3x  30  5x
30  2x
15  x
$15
Example 6: A clothing store drops the price of
a suit 25% to a sale price of $93. What was the
original price of the suit?
Heading: original price  x
sale price  x  .25 x
Equation:
(Solve)
Solution:
x  .25x  93
.75x  93
x  124
$124
Example 7:
An investment is made at 12% simple
interest. It grows to $812 at the end of one year. How
much was invested originally? Formula for final amount of
money (called “future value”): A = P + Prt
P is Principal; r is rate (%); t is time in years.
Heading:
Equation:
(Solve)
Solution:
Principal  P
812  P  P(.12)(1)
812  P  .12P
812  1.12P
725  P
$725
Example 8:
The sum of two consecutive even integers
is 50. What are the integers?
Heading:
Equation:
(Solve)
Solution:
x
x2
x  x  2  50
2x  2  50
2x  48
x  24
24 and 26
Example 9:
Find four consecutive integers such that
the sum of the second and fourth is 132.
Heading:
x
x 1
x2
x3
x  1  x  3  132
2x  4  132
(Solve)
2x  128
x  64
Solution: 64, 65, 66, 67
Equation:
Example 10:
The second angle of a triangle is four
times the first and the third is 5° more than twice the first.
Find the measures of the angles.
1st  x
The three angles of a triangle add up to 180°.
Heading:
Equation:
(Solve)
Solution:
2nd  4 x
3rd  5  2 x
x  4x  5  2x  180
5  7 x  180
7 x  175
x  25
25, 100, 55
Get ready for a “Small Quiz”
to be written
on your grade sheet.
Quiz. Copy the problems and write the
answer.
Solve:
1. ( x  4)( x  3)  0
3
5
3
3
2. x   10  x 
4
8
8
4
Put your grade paper on the front of
your row, quiz side down.
THE END