Dorthy is half her sisters age. She will be 3/4 her age in 20 years. How old is dorthy?

Question

dorothy is half her sisters age. she'll be 3/4 of her sisters age in 20 years. how old will she be

Answer 1

I'm not sure what level of math this is, but even if you don't know algebra, you can use algebra...

Write an algebra equation using "D" for Dorthy's age and "S" for her sister's age.

 

D = 1/2 S     Says Dorthy is 1/2 her sister's age.

 

20 years from now, Dorthy and her sister will be 20 years older and we will have:

 

(D + 20) = 3/4 (S + 20)   Which is saying Dorthy's age, 20 years from now is 3/4 of her sister's, 20 years from now.

 

Now with 2 equations and 2 unknown variables, you can solve with substitution:

 1.)  I multiply by 2 in the first equation so I can solve for S and it says S = 2D  (mostly so I don't have to plug in a fraction.)

 2.)  I plug in 2D for S in the second equation:      (D + 20) = 3/4 (2D + 20)

 3.)  I distribute the 3/4:                                     (D + 20) = 6/4 D + 3/4*20

 4.)  I reduce and simplify:                                   D + 20 = 3/2 D + 15

 5.)  I subtract D from both sides of the equation:         20 = 1/2 D + 15

 6.)  I subtract 15 from both sides of the equation:          5 = 1/2 D

 7.)  I multiply by 2:                                                    10 = D

 

So Dorthy's age is 10, she will be 30 in 20 years.

 

Check to make sure:

 -If Dorthy's 10 now, then her sister is 20. 

 -In 20 years, Dorthy will be 30 and her sister will be 40. 

 -30 is 3/4 of 40, so we are correct!