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
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
