Showing posts with label set theory. Show all posts
Showing posts with label set theory. Show all posts

Thursday, November 16, 2017

Sample Test on Set Theory

Sa mga sumasagot ng tanong sa ibaba, narito po ang solution at paliwanag:


Thirty five students went to the market. 27 of them bought mangoes and 32 bought bananas.

1. How many students bought mangoes only?
2. How many only bought bananas?
3. How many bought both mangoes and bananas?

Kapag ganito na ang birada ng tanong, dapat ay mag-assign agad tayo ng letter o representation para sa unknown.

Let       Z = number of students who bought mangoes and bananas

Let       27 – Z  = number of students who bought only mangoes

            Bakit ibabawas natin ang Z sa 27?

Para lumabas  ang mga students na bumili lamang ng mangga.

Let       32 – Z = number of students who bought only bananas

            Bakit ibabawas natin ang Z sa 32?

Para lumabas ang mga students na bumili lamang ng saging.

I-set up ang equation:

Z + (27-Z) + (32-Z) = 35

Bakit equals sa 35?

            Dahil 35 ang kabuuan ng mga mag-aaral.

Solve for Z:

Z + (27-Z) + (32-Z) = 35
-Z = 59 = 35
-Z = 35 – 59
-Z =  - 24

Multiply by (-1) to make the answer positive.

-1 x (-Z) = -1 X (-24)

Z = 24 ==> number of students who bought mangoes and bananas

27 – Z   = 27 – 24 = 3 ===> number of students who bought only mangoes

32 – Z = 32 – 24 = 8 ===> number of students who bought only bananas

24 + 3 + 8 = 35 ==> total number of students

Sana ay maunawaan at magamit sa test.