October 14, 2013
Two decreased by three times a number is eight
Two times the quantity three less than x is eight
Three times the number which is x less than two is
eight
October 14, 2013
Each car in a fleet of 24 rental cars is either red or
blue. There are 3 more blue cars than twice the
number of red ones. How many red cars there?
October 14, 2013
October 14, 2013
Review
combining like terms
Notes
2x + 3y - 5x + 8y
3x2 + 6x - 8x2- 9x
Distribution
Notes
3(2x + 5)
2x(4 - 3x)
-3(5x - 2)
Solving Equations
5x - 8 = 12
x + x+1 + x + 2 = 15
3(2x - 4) = 36
Notes
October 14, 2013
Directions: For each problem, (a) define the variable(s), (b) set up an equation, (c)
solve the equation and problem.
1. Suppose that Roni has twice as much money as Joe. Together they have $36.
How much money does each have?
2. A wooden board that is 60 inches long is sawn into to pieces. One piece is 4
inches longer than the other. What are the lengths of each piece of board?
3. There were 12 people on the jury. There were 4 more women than men. How
many women were on the jury?
4. The height of a tower is three times the height of a certain building. If the tower
is 50m taller than the building, how tall is the tower?
5. Kimberlee walked 8km more than Ed. Kimberlee walked twice as far as Ed.
How far did each of them walk?
October 14, 2013
6. A triangle has two equal sides and a third side that is 15cm long. If the perimeter
is 50 cm, how long is each of the two equal sides?
7. Ben has $23 more than Hannah. Together they have $187. How much does each
have?
8. The Little Lions won twice as many games as they lost. The played 96 games.
How many games did they win?
*9. The sum of three numbers is 120. The second of the numbers is 8 less than the
first, and the third is 4 more than the first. What are the numbers?
October 14, 2013
Examples:
a. Willy has $8 less than twice the amount of money Mackenzie
has. Willy has $34. How much does Mackenzie have?
b. Amanda read 2 more than 3 times as many books over the
summer than Mollie. Amanda read 17 books, how many did
Mollie read?
c. Tom knows 4 more than twice as many dances as Matt. Matt
knows 3 dances. How many does Tom know?
d. The sum of two consecutive integers is 85. What are the
integers?
e. The product of two consecutive numbers is 12. What are the
numbers?