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In Vs Dec
Ratios
Frac Bust Num/Vocab
5-D/Mat
QUESTION:
Decide if it is an increase or decrease and give the
percent of how much.
Joe is charging $13.00 a hour for his lawn care
company. He decides to up it to $18.00 a hour.
ANSWER:
It is a 38% increase
QUESTION:
Decide if it is an increase or decrease and give the
percent of how much.
The shirt is originally priced at $36.00 It then went
on sale for $23.00. What is the percent discount?
ANSWER:
It is a 36% discount
QUESTION:
Decide if it is an increase or decrease and give the
percent of how much.
Jim wants to enroll for a fitness class that normally
costs $50. There is a special price going on for $34.
ANSWER:
It is a 34% discount.
QUESTION:
Decide if it is an increase or decrease and give the
percent of how much.
Judy is buying a car for $24,000. The dealer tells
her the supercharged version costs only $3,000
more.
ANSWER:
It is a 12.5% increase
QUESTION:
Decide if it is an increase or decrease and give the
percent of how much.
Tim went to the store to buy milk for $4.69 It was
reduced to $3.72 for Friday and Saturday only.
ANSWER:
This is a 21% discount
QUESTION:
Mr. Anderson’s doctor has advised him
to go on a diet. He must reduce his
caloric intake by 15%. He currently
eats 2800 calories per day. Calculate
his new daily caloric intake rate.
ANSWER:
2380 calories per day
QUESTION:
Enrique is saving money to buy a
graphing calculator. So far he has
saved $30. His math teacher told him
he has saved 40% of what he will
need. How much does the calculator
cost?
ANSWER:
$75
QUESTION:
Amanda’s boat travels 35 miles per hour. The best fishing spot in the lake is
27 miles away from her starting point. If she drives her boat for 2/3 of an hour,
will she make it to the best fishing spot on the lake?
ANSWER:
She will not travel far enough
QUESTION:
Twenty-five percent of the students at
Marcus Garvey Middle School bring
their lunches from home. 285 students
do not bring their lunch. How many
students attend the school? Draw and
label a diagram to show the number
and percent of each group of students.
ANSWER:
QUESTION:
Liam was working on a problem and drew a diagram like the one
below. He then wrote the equation ($72)(0.14) = x. Does his equation
agree with his diagram? If Yes, then solve. If not explain what percent
of $72 he is looking for.
ANSWER:
14% is not the portion of $72 that is equal
to x in the diagram. He wants to find 86% of 72 to
get x or $72·0.86 = x, x = $61.92.
QUESTION:
Rewrite the equations below to make
them easier to solve.
0.04x + 0.16 = 0.06 + 0.08x
ANSWER:
4X + 16 = 6 + 8X
QUESTION:
Use the fraction buster method to solve this
problem.
3/2 + 2X/5 = 7/10
ANSWER:
X = -2
QUESTION:
The expression 3(x + 1) is a product, while 3x + 3 is a sum. For each
expression below, write an equivalent expression that is a product
instead of a sum. This process of writing an expression in the form of
factors (multiplication) is called factoring.
75X – 50
ANSWER:
25(3X-2)
QUESTION:
The expression 3(x + 1) is a product, while 3x + 3 is a sum. For each
expression below, write an equivalent expression that is a product
instead of a sum. This process of writing an expression in the form of
factors (multiplication) is called factoring.
-40m - 30
ANSWER:
-10(4m + 3)
QUESTION:
Solve the following equation:
ANSWER:
X=6
QUESTION:
Graph each of the following inequalities on a number line.
x<5
x > −4
ANSWER:
QUESTION:
Write the following expressions in one of two ways,
one with parentheses and one without.
A number increased by 7, then multiplied by 5.
Ten times a number, then add twenty.
ANSWER:
5(x + 7) = 5x + 35
10x + 20 = 10(x + 2)
QUESTION:
Solve the inequality. Represent the
solution algebraically (with symbols)
and graphically (on a number line).
3x − 3 < 2 − 2x
ANSWER:
QUESTION:
Use the words coefficient, constant,
term, expression, variable, and factor to
describe 4x2 + 11y −37.
ANSWER:
4 and 11 are coefficients; –37 is a constant
term; 4x2, 11y, and 37 are the three terms;
4x2 + 11y – 37 is an expression (but so are 4x2,
11y, and 37); x and y are variables.
QUESTION:
Use the words factor, product, quotient,
and sum to describe the parts of
ANSWER:
8 and m + n are factors of
8(m + n); 8(m + n) is a product; n is a
quotient; The entire expression is a
sum.
QUESTION:
Amelia wants to solve the equation shown on the Equation
Mat.
What is the solution to this equation? That is, what value
of x makes this equation true? Explain your reasoning.
ANSWER:
x = 0 because there are no tiles left on
the right side.
QUESTION:
Nick represented the equation 3(2x + 4)= −6 on
the Equation Mat below.
ANSWER:
X = -3
QUESTION:
Write an expression for each mat below. Simplify each mat to
determine which expression is greater, if possible. Justify your answer.
ANSWER: Mat A = 1
what X is equal to.
Mat B = X Depends on
QUESTION:
A triangle has a base that is three times longer than its
height. It has an area of 486 sq cm.
Use the 5-D Process to find the base and height of the
triangle. Write a variable expression for each column of
your table.
ANSWER:
Height = 18 cm and Base = 54 cm
QUESTION:
Solve the following word problems by writing and solving an
equation. You may choose to use the 5-D Process and create a table
to help you build your equation.
A Greenland whale can hold its breath three times as long as a beaver,
and a hippopotamus can hold its breath five minutes less than a
beaver. If you added the time a Greenland whale, beaver, and
hippopotamus can hold their breath, you would get 95 minutes! How
long can a beaver hold its breath?
ANSWER:
If x represents how long a beaver can hold its breath, then
3x + x + (x –5) = 95, 5x – 5 = 95, x = 20 minutes.