Day-2-Geometry.-Algebra-and-Problem-Solving (2).pdf

ALGEBRA, GEOMETRY,
PROBLEM-SOLVING

Question # 1
For what value of x will x be the
average of 2, 4x, 6, 8, 10?
D. 39
A. 4 C. 26
B. 12
C. 26

Question # 2
16 + 4 x (7 + 8) – 3 = ______.
D. 65
A. 117 C. 73
B. 145
C. 73

Question # 3
(18 + 17) (12 + 9) – (7 x 16) (4 + 2) = _____.
D. 323
A. 53 C. 321
B. 63
B. 63

Question # 4
What is the value of if ?
D. 3249
A. 43 C. 2451
B. 57
D. 3249
Note that:
By substitution:
𝟐 𝟐

Question # 5
What is the value of ?
D.
A. -125 C.
B. 125
C.
Rewrite the expression with a positive exponent:
(−5) =
1
(−5)
(−5) =
1
(−5)(−5)(−5)

Question # 6
The sum of three consecutive integers is 54.
Find the smallest integer
D. 19
A. 9 C. 17
B. 16
C. 17
𝑥 + (𝑥 + 1) + (𝑥 + 2) = 54
𝒙 = 𝟏𝟕
𝑥 + (𝑥 + 1) + (𝑥 + 2) = 54
Combine like terms to simplify the equation:
3𝑥 + 3 = 54
Subtract 3 from both sides:
3𝑥 = 51
Divide both sides by 3:
𝒙 = 𝟏𝟕

Question # 7
If the sum of 5 consecutive integers is 95.
What is the third number?
D. 19
A. 16 C. 18
B. 17
D. 19
(𝑥 − 2) + (𝑥 − 1) + 𝑥 + (𝑥 + 1) + (𝑥 + 2) = 95
𝒙 = 𝟏𝟗
The sum of these five integers is:
(𝑥 − 2) + (𝑥 − 1) + 𝑥 + (𝑥 + 1) + (𝑥 + 2) = 95
Simplify the equation by combining like
terms:
5𝑥 = 95
𝒙 = 𝟏𝟗

Question # 8
Four times the perimeter of a parking lot is 16
less than 2 000 meters. What is the perimeter
of the lot?
D. 1,008m
A. 496m C. 992m
B. 504m
D. 496m
4𝑃 = 2000 − 16
𝑃 =
4
𝑷 = 𝟒𝟗𝟔
4𝑃 = 2000 − 16
Simplify the right-hand side of the
equation:
4𝑃 = 1984
Now, divide both sides by 4 to solve for
𝑃:
𝑃 =
1984
4
𝑷 = 𝟒𝟗𝟔

Question # 9
The lengths of the sides of a triangle can be
represented by three consecutive integers. The
perimeter of the triangle is 96 cm. Find the length of
the longest side of the triangle.
D. 36
A. 28 C. 33
B. 32
C. 33
𝑥 + (𝑥 + 1) + (𝑥 + 2) = 96
𝑥 + 1 = 32
𝒙 + 𝟐 = 𝟑𝟑
𝑥 + (𝑥 + 1) + (𝑥 + 2) = 96
Combine like terms:
3𝑥 + 3 = 96
Subtract 3 from both sides:
3𝑥 = 93
Divide by 3:
𝑥 = 31
Therefore, the sides of the triangle are:
𝑥 = 31
𝑥 + 1 = 32
𝒙 + 𝟐 = 𝟑𝟑

Question # 10
The length of a rectangle is 8 meters more than twice
its width. The perimeter is 112 meters. Find its area.
D.
A. C.
B.
D.
𝑙 = 2𝑤 + 8
𝑃 = 2𝑙 + 2𝑤 = 112
𝑙 = 2(16) + 8
𝑙 = 40
𝑙 = 2𝑤 + 8
𝑃 = 2𝑙 + 2𝑤 = 112
By substitution:
2 2𝑤 + 8 + 2𝑤 = 112
4𝑤 + 16 + 2𝑤 = 112
6𝑤 = 112 − 16
6𝑤 = 96
𝑤 =
96
6
𝑤 = 16
𝑙 = 2(16) + 8
𝑙 = 40
To find the area:
𝐴 = 𝑙𝑤
𝐴 = 40 16
𝑨 = 𝟔𝟒𝟎 𝒎𝟐

Question # 11
The question “How many flowers are needed
to border a rectangular garden?”, involves:
D. area
A. weight C. volume
B. perimeter
B. perimeter
To determine how many flowers are
needed to border a rectangular garden,
you first need to calculate the perimeter
of the garden. The perimeter represents
the total length of the boundary where the
flowers will be placed. Once you have the
perimeter, you can then figure out how
many flowers are required based on the
spacing between them.

Question # 12
How many percent is the shaded
area?
D. 20%
A. 12% C. 14%
B. 12.5%
B. 12.5%
1
2 3
4
5
6 7
8

Question # 13
The difference between 8 times a number
and 17 is 231. Find the number
D. 1984
A. 31 C. 48
B. 37
A. 31
8𝑥 − 17 = 231
8
=
8
𝑥 = 31
8𝑥 − 17 = 231
Solve for x:
Add 17 to both sides of the equation:
8𝑥 = 231 + 17
8𝑥 = 248
8𝑥
8
=
248
8
𝑥 = 31

Question # 14
If 4 men can paint a fence in 2 days, what
part of the job can be completed by one man
in 8 days?
D. 1
whole job
A. C.
B.
D. 1 whole job

Question # 15
If 10 parts of alcohol is mixed with 15 parts of
water, what part of the mixture is alcohol?
D.
A. C.
B.
B.
Total parts = 10+15 = 25
Fraction of alcohol:

Question # 16
The amount of last month’s telephone bill, decreased
by the product of 3 and Php 30.00 equals Php 1,319.50.
Find the amount of the bill.
D. Php 1409.50
A. Php 1299.50 C. Php 1310.50
B. Php 1289.50
D. Php 1409.50
𝐵 − (3 × 30) = 1,319.50
𝐵 = 1,319.50 + 90
𝑩 = 𝟏, 𝟒𝟎𝟗. 𝟓𝟎
𝐵 − (3 × 30) = 1,319.50
Simplify and Solve the Equation:
Calculate the product:
3 × 30 = 90
Substitute into the equation:
𝐵 − 90 = 1,319.50
Add 90 to both sides to solve for B:
𝐵 = 1,319.50 + 90
𝑩 = 𝟏, 𝟒𝟎𝟗. 𝟓𝟎

Question # 17
The sale price of a television set is Php 7200. The
discount rate is 40%. Find its regular price
D. Php 12,000
A. Php 4320 C. Php 10,000
B. Php 6800
D. Php 12,000
The discount rate is 40%, so the
sale price is 60% of the regular price
(because 100% - 40% = 60%).

Question # 18
A trader bought a watch and sold it at 30% more
than its original cost. How much did the trader
earn if the original cost of the watch was P?
D. P + (P x 30%)
A. P + 30% C. 30% x P
B. 30%/P
C. 30% x P
Selling Price:
Earnings:

Question # 19
How much money can be saved by buying 70 pens at
Php 90 per dozen than buying them for Php 7.75?
D. Php 18.00
A. Php 0.25 C. Php 17.50
B. Php 12.00
C. Php 17.50
Cost per Pen:
Cost for 70 pens:
Cost for 70 pens (7.75 each):
Savings:

Question # 20
As a new typist, Rose can type only 2400 words
per hour. At the same rate, how many words can
she type in 30 minutes?
D. 1400
A. 1000 C. 1300
B. 1200
B. 1200

Question # 21
Milo can paint the ceiling of a studio-type room in 30
minutes while Moby can do the job in 20 minutes. If
they work together, how long will it take them to
finish the job?
D. 24 mins.
A. 10 mins. C. 18 mins.
B. 12 mins.
B. 12 mins

Question # 22
When a number is decreased by 5 and multiplied
by 2, the result is 30. Find the number.
D. 25
A. 10 C. 20
B. 18
C. 20
Distribute the 2:
Add 10 to both sides:
Divide by 2:

Question # 23
Milo is 5 years older than Moby. Three years
ago, he was twice as old as Moby. How old is
Moby now?
D. 30
A. 6 C. 15
B. 8
B. 8

Question # 24
Six years ago, Mark was four times as old as Flor.
In 4 years, he will be twice as old as Flor. How
old is Mark now?
D. 52 y.o
A. 20 y.o C. 36 y.o
B. 26 y.o
B. 26 y.o 𝑀 = 2𝐹 + 4
𝑴 = 𝟐 𝟏𝟏 + 𝟒 = 𝟐𝟔 𝒚𝒆𝒂𝒓𝒔 𝒐𝒍𝒅
Let M be Mark’s current age and F be Flor’s current age
Age six years ago:
𝑀 − 6 = 4 𝐹 − 6 → 𝑀 = 4𝐹 − 18
Age in four years:
𝑀 + 4 = 2 𝐹 + 4 → 𝑀 = 2𝐹 + 4
Equate the two:
4𝐹 − 18 = 2𝐹 + 4
2𝐹 = 22
𝐹 = 11
Therefore, Mark’s age is:
𝑀 = 2𝐹 + 4
𝑴 = 𝟐 𝟏𝟏 + 𝟒 = 𝟐𝟔 𝒚𝒆𝒂𝒓𝒔 𝒐𝒍𝒅

Question # 25
A man invested at Php 100,000. He put part of it in a bank at 5%
interest. On the other hand, he invested the remainder in bonds
with a 9% yearly return. How much did he put in the bank if his
yearly income from the two investments was Php 7,400?
D. Php 70,000
A. Php 40,000 C. Php 60,000
B. Php 50,000
A. Php 40,000

Question # 26
Sophia obtained the following results from her
mathematics exams: 80, 82, 83, 91. What score must she
get on the next exam so that her average score is 85?
D. 93
A. 85 C. 92
B. 89
B. 89

Question # 27
In a Filipino test, eight students obtained the
following scores 10, 15, 12, 18, 16, 24, 12, 14.
What is the median score?
D. 15.5
A. 14 C. 15
B. 14.5
B. 14.5

Question # 28
If it takes four fire fighters 1 hour and 45 minutes to
perform a job, how long would it take one firefighter
working at the same rate to perform the task alone?
D. 7.5 hours
A. 4.5 hours C. 7 hours
B. 5 hours
C. 7 hours

Question # 29
It takes 16 hours for 2 men to resurface a gym floor. At
the same rate, how long would it take 8 people?
D. 64 hours
A. 4 hours C. 16 hours
B. 8 hours
A. 4 hours

Question # 30
The average weight of A, B and C is 45 kg. If the
average weight of A and B be 40 kg and that of B and C
be 43 kg, then the weight of B is:
D. 31 kg
A. 17 kg C. 26 kg
B. 20 kg
D. 31 kg

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