La suma de las edades de una madre y de su hijo son 56 años. Hace 10 años, la edad de la madre era el quíntuple de la edad que tenía el hijo. ¿Cuál es la edad actual de cada uno?

The mother is 40 years old and the son is 16 years old.

Step-by-step explanation:

With a system of equations mentioned in the statement the answer can be reached, we have to:

Let X be the age of the mother, Y the age of the son.

X + Y = 56 (1)

X-10 = 5 * (Y-10) (2)

Solving

 X -10 = 5 * Y - 50

From where:

X = 5 * Y - 40

Substituting in the first equation:

5 * Y - 40 + Y = 56

6 * Y = 56 + 40

Y = 96/6 = 16

Now, replacing the value of Y:

X = 5 * 16 - 40

X = 80 -40

X = 40

Therefore the mother is 40 years old and the son is 16 years old.

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)

step-by-step explanation:

no, her answer is not correct.   we square the lengths of all sides and then determine whether the pythagorean theorem holds here:

9² + 15² = 306.   this is not equal to the square of the longest side ( that square being 395.   answer c is correct.