This document contains 10 math word problems. For each problem, the student is asked to identify an unknown percentage, calculate it, and show the work. The problems cover topics like discounts, taxes, tips and calculating percentages of totals. The student's work and solutions are written in below the problems.
To solve __% of A is B.
Change:
__ to x,
of to * (multiplication)
is to =
Do the algebra to solve the equation.
Write x as a percent.
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To solve __% of A is B.
Change:
__ to x,
of to * (multiplication)
is to =
Do the algebra to solve the equation.
Write x as a percent.
Learnist Board: http://bit.ly/13AGhZq
More information at http://bit.ly/ZXLw0I
#P10
Name _________________________ Score ______ ______1..docxlea6nklmattu
Name: _________________________
Score: ______ / ______
1.
Find the indicated sum. Show your work.
k = 1, (-1)^k (k + 11) = (-1)^(1) (1 + 11)= -1*(12) = -12
k = 2, (-1)^k (k + 11) = (-1)^(2) (2 + 11)= 1*(13) = 13
k = 3, (-1)^k (k + 11) = (-1)^(3) (3 + 11)= -1*(14) = -14
k = 4, (-1)^k (k + 11) = (-1)^(4) (4 + 11)= 1*(15) = 15
(-12)+(13)+(-14)+(15)=2
2.
Locate the foci of the ellipse. Show your work.
X^2=(x-h)^2, then h=0
Y^2=(x-k)^2, then k=0
The centre is (0,0)
X^2/36+y^2/11=1
When x=0 y^2/11=1; y=0
When y=0,x=0
X^2/36=1;x=0
11+c^2=36
C=5
Foci (5,0) and (-5,0)
3.
Solve the system by the substitution method. Show your work.
2y - x = 5
x2 + y2 - 25 = 0
x:
2y - x = 5
2y - 5 = x
so x = 2y - 5
-Plug this into 2nd equation:
(2y - 5)² + y² - 25 = 0
-Use FOIL to solve the (2y - 5)² part:
(2y - 5)(2y - 5)
4y² - 10y - 10y + 25
4y² - 20y + 25
So :
4y² - 20y + 25 + y² - 25 = 0
Which can be simplified to:
4y² + y² - 20y = 0
4y² + y² - 20y = 0
y(4y + y - 20) = 0
So, because of the 0 multiplication rule,
y=0
x= -5 (plug in y=0 to original equations:
2y - x = 5
2(0) - x = 5, so x= -5)
(-5,0)
Y(4y+y-20)=0
So, y=0 or 4y+y-20=0
5y-20=0
Y=4
X=2y-5 when y=4
X=8-5=3
(-5,0) (3,4)
4.
Graph the function. Then use your graph to find the indicated limit. You do not have to provide the graph
f(x) = 5x - 3,
f(x)
22
5.
Use Gaussian elimination to find the complete solution to the system of equations, or state that none exists. Show your work.
4x - y + 3z = 12
x + 4y + 6z = -32
5x + 3y + 9z = 20
6.
Solve the system of equations using matrices. Use Gaussian elimination with back-substitution.
x + y + z = -5
x - y + 3z = -1
4x + y + z = -2
X=1/3, y=-(11/3),z=-(5/3)
7. A woman works out by running and swimming. When she runs, she burns 7 calories per minute. When she swims, she burns 8 calories per minute. She wants to burn at least 336 calories in her workout. Write an inequality that describes the situation. Let x represent the number of minutes running and y the number of minutes swimming. Because x and y must be positive, limit the boarders to quadrant I only.
7x+8y>=336
Short Answer Questions:
Type your answer below each question. Show your work.
8.
A statement S
n
about the positive integers is given. Write statements S
1
, S
2
, and S
3
, and show that each of these statements is true.
Show your work.
S
n
: 1
2
+ 4
2
+ 7
2
+ . . . + (3n - 2)
2
=
S1=1(6*1^2-3(1)-1)/2=1
S2=1^2+4^2=17
S31^2+4^2+7^2=66
9.
A statement
S
n
about the positive integers is given. Write statements
S
k
and
S
k+1
, simplifying
S
k+1
completely. Show your work.
S
n
: 1 ∙ 2 + 2 ∙ 3 + 3 ∙ 4 + . . . +
n
(
n
+ 1) = [
n
(
n
+ 1)(
n
+ 2)]/3
10.
Joely's Tea Shop, a store that specializes in tea blends, has available 45 pounds of A grade tea and 70 pounds of B grade tea. These will be blended into .
The above is the part of Quantitative Aptitude, it is just a topic name "Percentages". From this you can easily learn few basics of how numericals of mathematics that to be dealt with few shortcuts. I hope this will be useful for everyone to understand few things about Quantitative Aptitude. Specially this is for the persons who are preparing for the competative exams.
2. Name __________________________________________________ Date _________________________
Mrs. Labuski / Mrs. Rooney Period _____________ Homework & Practice 8-10
PLEASE SHOW ALL YOUR WORK BELOW!!!
1. 2.
is = % is = %
of 100 of 100
3. 4.
is = % is = %
of 100 of 100
3. 5. 6.
is = % is = %
of 100 of 100
7. 8.
is = % is = %
of 100 of 100
6. Name __________________________________________________ Date _________________________
Mrs. Labuski / Mrs. Rooney Period _____________ Homework & Practice 8-10
PLEASE SHOW ALL YOUR WORK BELOW!!!
1. 2.
is = % is = %
of 100 of 100
$18.62 necklace
+$ 7.98 ring
x = 22 26.6 total cost
105.36 100
is = %
100x = 2317.92 of 100
÷100 ÷100
x = 23.1792 x = 35
(can’t have 4 digits after decimal for money so 26.6 100
round to the hundredths)
$23.1792= 23.18 100x = 931 $20.00 bill
$23.18 = tip ÷100 ÷100 -$17.29 price
x = 9.31 $2.71 change
$9.31 = discount Answer: $2.71 change
$26.60 total cost
-$ 9.31 discount
$17.29 = new price
3. 4.
is = % is = %
of 100 of 100
x = 15
x = 8__ 13.27 100
18000 100
100x = 199.05
100x = 144000 ÷100 ÷100
÷100 ÷100 x = 1.9905
x = 1,440 (can’t have 4 digits after decimal for money so
round to the hundredths)
$1.9905 = $1.99
$1.99 = discount
goal: 18,000
extra: + 1,440 $13.27 = lunch
$19,440 total raised -$ 1.99 = discount
$11.28 = total bill after discount
7. 5. 6.
is = % is = %
of 100 of 100
x = 26
51.23 100 x = 18
16.78 100
100x = 1331.98
÷100 ÷100 100x = 302.04
x = 13.3198 ÷100 ÷100
(can’t have 4 digits after decimal for money so x = 3.0204
round to the hundredths) (can’t have 4 digits after decimal for money so
$13.3198 = $13.32 = discount round to the hundredths)
$3.0204= 3.02
$51.23 = bouquet $3.02 = tip
-$13.32 = discount
$37.91 = total bill after discount $16.78 = pizzas
+$3.02 = tip
$19.80 = total to give to delivery man
7. 8.
is = % is = %
of 100 of 100
x = 8.5 x = 6
258.98 100 84.21 100
100x = 2201.33 100x = 505.26
÷100 ÷100 ÷100 ÷100
x = 22.0133 x = 5.0526
(can’t have 4 digits after decimal for money so (can’t have 4 digits after decimal for money so
round to the hundredths) round to the hundredths)
$22.0133 = $22.01 $5.0526 = 5.05
$ 22.01 = tax $5.05 = tax
$258.98 = television $84.21 = bike
+$22.01 = tax +$5.05 = tax
$280.99 = total cost $89.26= total cost
8. 10.
is = %
of 100
x = 35
15 100
100x = 525
÷100 ÷100
x = 5.25 = discount
$15.00 = book
-$ 5.25 = discount
Skip #9!!!
$9.75 = cost of book after discount
is = %
of 100
x = 9
9.75 100
100x = 87.75
÷100 ÷100
x = .8775 = tax
(can’t have 4 digits after decimal for money so
round to the hundredths)
x = .8775 = x = .88