how did you determine your answer?

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Math Bowl
Let’s get ready to………
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Question 1
• Maria is making blueberry muffins, using a
blueberry cake recipe. To make the muffins,
she needs to divide the recipe in half. If the
recipe calls for 1 2/3 cup of milk, how much
milk will she need to make the muffins?
Solution #1
She would use 5/6 cup of milk to make the
muffins.
Show your work:
2 5
1 
3 3
5 2
 
3 1
5 1 5
 
3 2 6
Question 2
Kara saved $36 of the $80 she earned
babysitting. What percent of her earnings did
Kara save?
Solution #2
• Kara saved 45% of her earnings
• Show your work:
36 x

80 100

• Set up a proportion.
• Cross multiply.
• Use the inverse operation of
multiplication (division).
• Divide and solve for x.
80x  3600
x  3600 80
x  45
• IS THERE ANOTHER WAY TO FIND THE
VALUE OF X IN THIS PROPORTION?
Question 3
Square QRST has the following vertices:
Q(2,8), R(-4,8), S(-4, 2), and T(2,2).
Triangle QTU has the vertices:
Q(2,8), T (2,2), and U(6,2).
What is the area of the quadrilateral formed by the
square and the triangle?
Solution #3
SQUARE: One side of the square measures 6 units.
Q(2,8) and R (-4, 8) The y-values are the same, so I added
the absolute values of 2 and -4.
|2|= 2
|-4| = 4
2 + 4= 6
Area of square QRST: 6 x 6 = 36 sq. units
The height of the triangle is 6 and the base is 4
units.
TRIANGLE: Area of Triangle QTU: 6 x 4 / 2= 12 sq. units
36 = 12 = 48
ANSWER: 48 sq. units
Question 4
Part A: Which expression is equivalent to 4- 8x?
a)
b)
c)
d)
4(1-8x)
2(2-4x)
4(4-2x)
2(1-4x)
Part B: Tell how you determined your answer.
Solution #4
Choice a is correct.
4(1-8x)
How did you determine your answer?
Question 5
A side of a regular hexagon measures 5 cm. A
line segment was drawn from the center of
the hexagon to the middle of the bottom side.
What is the area of this hexagon?
HINT: Draw a sketch of this hexagon first.
Solution #5
A= 64.5
2
cm.
HOW DID YOU SOLVE THIS
PROBLEM?
Question 6
The product of two factors is 18x + 45. What are
the factors?
a)
b)
c)
d)
9(5x + 2)
9(2x + 5)
3(2x + 15)
3(6x-5)
Solution #6
Choice B: 9(2x + 5)
HOW DID YOU DETERMINE YOUR
ANSWER?
Question 7
• A can of tomato soup has a net weight of 8
ounces. How many grams are in the can of
soup?
1 ounce = 28.35 grams
Solution #7
226.8 grams
HOW DID YOU DETERMINE
YOUR ANSWER?
Question 8
Shayla bought 2.75 liters of cranberry juice,
3.5 liters of pineapple juice, and
4.2 liters of orange juice for punch for a party.
How many liters of punch will this make
altogether?
Solution #8
10.45 L
Show your work:
2.75
3.50
* Remember to line up your decimals!
+ 4.20
10.45 or 10.45 Liters
Question #9
Sam needs at least 78 credits to get his
college degree. At the end of his third
year, Sam has a total of 52 credits.
Part A: Write an inequality that represents
how many more credits, C, Sam needs to
get his degree?
Part B: Graph the inequality on a number
line.
Solution #9
c 26
EXPLAIN HOW YOU MADE YOUR GRAPH ON A
NUMBER LINE.
Question 10
A shipping container in the shape of a
rectangular prism, fits in a space that
has a volume of 2,212 cubic meters.
If the container is 7 meters wide and
8 meters tall, how long is the
container?
Solution #10
• The shipping container is 39.5
meters long.
• HOW DID YOU DETERMINE YOUR
ANSWER?
Question 11
Part A: Write an expression for the
following statement:
A number multiplied by 4, subtracted
from 65.
Part B: Can an equivalent expression
be written for the expression?
Explain.
Solution #11
Part A: 65-4x
Part B: You cannot write an
equivalent expression because
order matters in subtraction and
there aren’t an common factors
of the two terms.
Question 12
The graph below shows the amount of money earned during a
car wash held at Sweet Home Middle School last Saturday.
Write an equation to determine the relationship between the
number of hours (x) and the amount of money raised (y).
Solution #12
y= 10x
I used the coordinates (1,10),
(2,20), (3,30), (4,40), and so on
to determine the relationship
between x and y.
Question 13
Stephanie drove 16 miles less than
three times the distance Jaydah
drove. Use j for the number of miles
Jaydah drove. Write an expression
for the number of miles Stephanie
drove.
Solution #13
3j-16
Question 14
Evaluate for a = 3.
14  (5  a)  (6  2)
2
2
2
Solution #14
208
HOW DID YOU
DETERMINE YOUR
ANSWER?
Question 15
In art class, 40% of the students used
watercolors for painting. Ten students in
art class used watercolors. How many
students were in the art class?
Solution #15
25 students used watercolors.
HOW DID YOU DETERMINE
YOUR ANSWER?
Question 16
Andrew had $250 in his savings account. He
deposited the same amount of money for
each of the next 6 weeks. For the next 4
weeks, he deposited twice the amount of
money as the previous six weeks. If d is the
amount of money Andrew deposited each
week, write an expression to represent how
much money he will have in his account after
the tenth week.
Solution #16
250+d+4(2d)
Question 17
Mrs. Bogacz burns 90 calories
walking in ten minutes. At this
rate, how many calories will she
burn in 16 minutes?
Solution #17
Question 18
Which expression is equivalent to
a + a + a + b + b+ b?
a) 3a + b
b) a3 + b3
c) 3a + 3b
d) 3 + ab
Solution #18
Choice C is correct.
3a + 3b
Question 19
Stephon has a 22.74 liter container of water.
How many gallons is this container?
1 gallon = 3.79 liters
Solution #19
6 gallons
How did you determine your answer?
Question 20
The table below lists places around the
world that have land areas below sea level.
If sea level is 0, which place is closest to sea level?
Country
Death Valley, United
States
Lake Eyre, Australia
Lake Enriquillo
Laguna Salada, Mexico
Elevation
-86 meters
-16 meters
-46 meters
-10 meters
Solution #20
Laguna Salada, Mexico
Question #21
Consider the following expression: 4(7x + 5)
Part A: Write two equivalent expressions for it using
two different properties.
Part B: Tell which property you used for each
expression in Part A.
Part C: How many factors does 4(7x+5) have?
What number is a coefficent in the expression?
Solution #21
Part A and B:
28x + 20- distributive property
(7x+5)4- commutative property
Part C:
There are two factors in the expression 4(7x + 5).
The coefficient is 7.
Question #22
Two vertices of a right triangle are (0,1) and
(0,6). The area of the triangle is 10 square
units. Which point in Quadrant II is the
third vertex of the triangle?
Solution #22
(-4, 1)
Question #23
• There are 40 cups of flour in a bag. If 25% of
the flour is used to make 2 batches of cookies,
how many cups of flour was used?
Solution # 23
10 cups
Show your work:
The total is 40 cups of
flour.
25% of the total
.25 x 40
25% = .25
40
x .25
200
+ 800
10.00
Move the decimal 2
places to the left
Remember:
% of the total
‘MULTIPLY’
Question 24
Tyler charted the amount of water he drank in
the last 30 days. Based on the data in the
table, what is the probability that he will drink
more than 30 ounces of water in a day?
Number of days Amount of
water he drank
6
0-10 ounces
11
11- 20 ounces
3
21- 30 ounces
6
31-40 ounces
4
41 or more
ounces
Solution #24
Answer: 1/3
Show your work:
6 days he drank 30 oz
Number of days
4 days he drank 40 + oz
6
11
Part
10 days
3
Whole 30 days
6
4
Amount of
water he drank
0 -10 ounces
11 - 20 ounces
2 1- 30 ounces
31 - 40 ounces
41 or more
ounces
Question #25
Find the area and perimeter of this figure.
7 feet
6 feet
2 feet
10 feet
Solution #25
Show your work:
A=lxw + A=lxw
P=s+s+s+s+s+s
8x7
+
3x2
8 + 7 + 6 + 3 + 2 + 10
56
+
6
AREA = 62 sq feet
PERIMETER = 36 feet

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