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Polya s problem solving strategy

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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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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 ...
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