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NAME: Morillo B. Morillo
COURSE/YEAR/SECTION:BSA 1A
DATE:September 10, 2020
SOLUTION TO EXERCISE 3.4 POLYA’S PROBLEM SOLVING STRATEGY
2. Mr. Procopio has many animals on his farm. He has 72 chickens, which make up 60% of his
total animals, and the rest of his animals are goat. How many legs in total do his animals have?
Let: x = number of chickens
y = number of goats
n = number of legs
Clue: Chicken has two (2) feet and goat has four (4) feet.
Ist equation (60%)x = 72
2nd equation y = x 72
3rd equation n = 72(2) + y(4)
Solve:
(60%)x = 72 y = x 72 n = 72(2) + y(4)
0.6x = 72 y = 120 72 n = 72(2) + 48(4)
0.6 0.6
y = 48 n = 144 + 192
x = 120
n = 336
Therefore: The total number of the feet of the chickens is 144.
The total number of the feet of the goats is 192.
The total number of the feet of these animals are 336.
4. The length of the rectangular lot is four times its width. If the length is increased by 6 feet
and the width is decreased by 3 feet, the area of the lot is decreased by 23 square feet. Find the
dimension of the rectangle.
Let: Width = x
Lenght = 4x
Area = 4x (x) 23
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Solve:
4x (x) 23 = (4x + 6) (x 3) Lenght = 4x
4x
2
23 = 4x
2
6x 18 = 4 (
󰇜
-23 + 18 = 4x
2
4x
2
6x =

or

feet
-5 = -6x


=


Width
= x
Therefore: The dimension of the rectangle is
width and

feet.
6. If 384 is 60% of x, What is the value of x?
Equation: 384 = (60%)x
Solve:
384 = (60%)x
384 = (0.6)x
0.6 0.6
640 = x
To check, substitute the value of x in the equation.
384 = (60%)x
384 = (60%) 640
384 = 384
Therefore: The value of x is 640.
8. Find the present value of Php 6,500.00 which is due at the end of 4 years if the interest rate is
6.5 %.
Let:
PV = present value
FV = future value
n = number of periods
r = interest rate
Formula: FV = P (1 + r)
n
Solve:
₱6,500 = PV (1 + 0.065)
4
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󰨷
󰇛

󰇜
= PV [Divide both sides by (1 + 0.065)
4
]
󰨷

= PV
5,052.60 = PV
To check, substitute the value of PV in the equation.
FV = P (1 + r)
n
₱6,500 = ₱5,052.60 (1 + 0.065)
4
₱6,500 = ₱6,500
Therefore:
The presenr value of Php 6,500 that is due in 4 years with an interest rate of 6.5% is Php 5,052.60.
10. The length of rectangular frame is 8 inches longer than twice the width. If the perimeter is 100
inches. What are the frames dimension?
Let: Width = w
Lenght = 2w + 8
Perimeter = 100
Solve:
100 = 2w + 2 (2w +8) L = 2w + 8
100 = 2w + 4w +16 L = 2(14) + 4
100 16 = 2w + 4w L = 28 + 8
84 = 6w L = 36
6 6
14 = w
To check, substitute the value of w and L.
100 = 2w + 2l W = 14
100 = 2(14) + 2(36) L = 36
100 = 28 + 72
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100 = 100
Therefore: The dimension of the frames are 14 width and 36 lenght.

Unformatted Attachment Preview

NAME: Morillo B. Morillo COURSE/YEAR/SECTION:BSA 1A DATE:September 10, 2020 SOLUTION TO EXERCISE 3.4 POLYA’S PROBLEM SOLVING STRATEGY 2. Mr. Procopio has many animals on his farm. He has 72 chickens, which make up 60% of his total animals, and the rest of his animals are goat. How many legs in total do his animals have? Let: x = number of chickens y = number of goats n = number of legs Clue: Chicken has two (2) feet and goat has four (4) feet. Ist equation 2nd equation 3rd equation (60%)x = 72 y = x – 72 n = 72(2) + y(4) Solve: (60%)x = 72 y = x – 72 n = 72(2) + y(4) 0.6x = 72 0.6 0.6 y = 120 – 72 n = 72(2) + 48(4) y = 48 n = 144 + 192 x = 120 n = 336 Therefore: The total number of the feet of the chickens is 144. The total number of the feet of the goats is 192. The total number of the feet of these animals are 336. 4. The length of the rectangular lot is four times its width. If the length is increased by 6 feet and the width is decreased by 3 feet, the area of the lot is decreased by 23 square feet. Find the dimension of the rectangle. Let: Width = x Lenght = 4x Area = 4x (x) – 23 Solve: 4x (x) – 23 = (4x + 6) (x – 3) Lenght = 4x 𝟓 4x2 – 23 = 4x2 – 6x – 18 =4( ) -23 + 18 = 4x – 4x – 6x -5 = -6x −5 −6x = 2 −6 2 = 𝟐𝟎 𝟔 𝟔 or 𝟏𝟎 𝟑 feet −6 𝟓 Width 𝟔 = x 𝟓 Therefore: The dimension of the rectangle is 𝟔 width and 10 3 feet. 6. If 384 is 60% of x, What is the value of x? Equation: 384 = (60%)x Solve: 384 = (60%)x 384 = (0.6)x 0.6 0.6 640 = x To check, substitute the value of x in the equation. 384 = (60%)x 384 = (60%) 640 384 = 384 Therefore: The value of x is 640. 8. Find the present value of Php 6,500.00 which is due at the end of 4 years if the interest rate is 6.5 %. Let: PV = present value FV = future value n = number of periods r = interest rate Formula: FV = P (1 + r) n Solve: ₱6,500 = PV (1 + 0.065) 4 ₱6,500 (1+0.065)4 [Divide both sides by (1 + 0.065) 4] = PV ₱6,500 1.28646635062 = PV ₱5,052.60 = PV To check, substitute the value of PV in the equation. FV = P (1 + r) n ₱6,500 = ₱5,052.60 (1 + 0.065) 4 ₱6,500 = ₱6,500 Therefore: The presenr value of Php 6,500 that is due in 4 years with an interest rate of 6.5% is Php 5,052.60. 10. The length of rectangular frame is 8 inches longer than twice the width. If the perimeter is 100 inches. What are the frames dimension? Let: Width = w Lenght = 2w + 8 Perimeter = 100 Solve: 100 = 2w + 2 (2w +8) 100 = 2w + 4w +16 100 – 16 = 2w + 4w 84 = 6w 6 6 L = 2w + 8 L = 2(14) + 4 L = 28 + 8 L = 36 14 = w To check, substitute the value of w and L. 100 = 2w + 2l W = 14 100 = 2(14) + 2(36) L = 36 100 = 28 + 72 100 = 100 Therefore: The dimension of the frames are 14 width and 36 lenght. Name: Description: ...
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