Question

Las edades de dos hermanos tienen una razón de 2 a 1. Cuando transcurran 4 años, la razón entre sus edades será de 8 a 6. ¿Cuántos años tienen actualmente?

Answer 1

Answer:

The age of brothers are 4 years and 2 years respectively.

Step-by-step explanation:

We are given that the ages of two brothers have a ratio of 2 to 1. When 4 years have passed, the ratio of their ages will be 8 to 6.

Let the age of the first brother be 'x years' and the age of the second brother be 'y years'.

So, according to the question;

• The first condition states that the ages of two brothers have a ratio of 2 to 1, that means;

                                      $\frac{x}{y} =\frac{2}{1}$  

                                      $x=2y$  -------------- [equation 1]

• The second condition states that when 4 years have passed, the ratio of their ages will be 8 to 6, that means;

                                       $\frac{x+4}{y+4}=\frac{8}{6}$

                               $6({x+4})=8}(y+4)$

                               $6x+24=8y+32$

                               $6(2y)+24=8y+32$

                               $12y-8y=32-24$

                                    $4y=8$

                                     $y=\frac{8}{4}$ = 2 years

Putting the value of y in equation 1 we get;

                                     x = 2y

                                      x = $2 \times 2$ = 4 years

Hence, the age of brothers are 4 years and 2 years respectively.