Chapter 6 Study guide .
Name _____________
score ______
Practice
Your teacher is giving you a test worth 100 points containing 40 questions. There are two‐
point and four‐point questions on the test. How many of each type of question are on the
test?
Sally has 20 coins in her piggy bank, all dimes and quarters. The total amount of money is
$3.05. How many of each coin does she have?
A farmer has 10 animals, they are either ducks or pigs. If his animals collectively have 32
feet, how many pigs does he have? How many ducks does he have?
A large McDonald’s chocolate milkshake has 720 more calories than a double
cheeseburger. Two double cheeseburgers and the large chocolate shake have a total of
2040 calories. How many calories are in each item?
Suppose you are starting an office‐cleaning service. You have spent $315 on equipment.
To clean an office, you use $4 worth of supplies. You charge $25 per office. How many
offices must you clean to break even?
Determine if a system of equations is consistent (has 1 or infinite solutions) or not
consistent ( has 0 solutions)
Consistent 1 solution
Y= 2x + 1
Y=3x
Consistent infinite
solutions
2x + 3y =6
4x + 6y = 12
Two lines on top of each
other
Not consistent zero
solutions
2x + 5y =10
2x +5y = 12
Substitution
2x+1 =3x
Elimination
-4x -6y = -12
4x + 6y = 12
Elimination
2x+5y=10
-2x -5y = -12
0=0
0 = -2
One equation is the
same as the other only
written differently. All
solutions are the same.
The equations have the
same slope but a
different y intercept.
They are parallel and
will never intersect.
Graphs
Algebra
x=1 y=3
(1,3)
The equations have
Structure different slopes. This
in the
means they will
equation eventually intersect at
a point.
Tell how many solutions each system of equations has zero, infinite or one.
Extra practice with word problems
The local preschool ordered all new bicycles and tricycles for the new school year. Each
bicycle and tricycle is shipped in its own box. Oddly, the manufacturer shipped all the
wheels in a separate box. If there are 16 boxes of bicycles/tricycles total, and 45 wheels
total, how many tricycles were ordered?
A McDonald’s apple pie has 90 more calories than their chocolate chip cookie. Two apple
pies and three cookies have a total of 980 calories. How many calories are in each item?
Nate Kaeding, the place kicker for the San Diego Chargers, has scored 120 so far this
season. He has scored all his points on 1‐point extra point kicks and 3‐point field goals. He
has made a total of 66 kicks. How many of each kick has he made?
A Honda dealership sells both motorcycles and cars. There are a total of 200 vehicles on
the dealership’s lot. The detailer cleaned all the wheels of all the vehicles, which totaled
698 wheels. How many motorcycles are there on the lot?
At The Apple Pan, two burgers and three orders of fries cost $19.75. Five burgers and two
orders of fries cost $37. What is the cost for a burger and an order of fries?
At the Apple Pan, three steakburgers and two orders of fries cost $18. Two steakburgers
and three orders of fries cost $15.75. What is the cost for one steakburger?
Complementary angles are two angles that add up to 90 degree. One angle is twice as big
as its complement. What are the measures of the two angles? Come up with some
equations to show your work.
Supplementary angles are angles that add up to 180 degrees. One angle is 30 less than 2
times the other angle. What are the angle measures?