Question

Las edades de paulina y monica suman 36, las de monica y andrea 40, mientras que la suma de las edades de paulina y andrea es 44¿Cuantos años tiene cada una?

Answer 1

The question in English is

The ages of Paulina and Monica are 36, the ages of Monica and Andrea 40, while the sum of the ages of Paulina and Andrea is 44. How old is each one?

Let

x------> Paulina's age

y------> Monica's age

z------> Andrea's age

we know that

x+y=36--------> equation 1

y+z=40--------> y=40-z--------> equation 2

x+z=44--------> x=44-z--------> equation 3

Substitute equation 2 and equation 3 in equation 1

[44-z]+[40-z]=36

84-2z=36

2z=84-36

z=48/2-------> z=24 years

Find the value of x

x=44-z-------> x=44-24------> x=20 years

Find the value of y

y=40-z-----> y=40-24------> y=16 years

therefore

the answer is

Paulina's age is 20 years old

Monica's age is 16 years old

Andrea's age is 24 yeras old

The answer in Spanish

Hagamos

x------> La edad de Paulina

y------> La edad de Monica

z------> la edad de Andrea

Sabemos que

x+y=36--------> ecuacion 1

y+z=40--------> y=40-z--------> ecuacion 2

x+z=44--------> x=44-z--------> ecuacion 3

sustituya ecuacion 2 y ecuacion 3 en la ecuacion 1

[44-z]+[40-z]=36

84-2z=36

2z=84-36

z=48/2-------> z=24

Encuentre el valor de x

x=44-z-------> x=44-24------> x=20

Encuentre el valor de y

y=40-z-----> y=40-24------> y=16

por lo tanto

La respuesta es

La edad de Paulina es igual a 20

La edad de Monica es igual a 16

La edad de Andrea es igual a 24

Answer 2

Defining variables we have:

x: Paulina's age

y: Age of monica

z: Age of Andrea

We write the system of equations:

The ages of Pauline and Monica sum 36:

x + y = 36

Monica and Andrea 40:

y + z = 40

the sum of the ages of Pauline and Andrea is 44:

x + z = 44

From equation three we have:

z = 44-x

From equation 2:

y + z = 40

y + (44-x) = 40

y = 40-44 + x

y = -4 + x

From equation 1:

x + (- 4 + x) = 36

2x = 36 + 4

2x = 40

x = 20

Then, the age of monica is:

y = -4 + x

y = -4 + 20

y = 16

Finally, Andrea's age is:

z = 44-x

z = 44-20

z = 24

Answer:

Paulina is 20 years old

Monica is 16 years old

Andrea is 24 years old