A girl is 2/3 as old as her brother in 5 years. 3 years ago she was 1/2 as old as her brother. How old is she now

Question

This is an age problem. Please help ASAP

Answer 1

We have 2 unknowns: the present age of the girl and the present age of her brother. For 2 unknowns, we need 2 equations in order to solve this.

Let x = the age of the girl

y = the age of her brother

Eq. I: x + 5 = (2/3)(y + 5)

Eq. II: x - 3 = (1/2)(y - 3)

We can use either the substitution or the elimination to solve for this. Let's use elimination by subtracting Eq. II from Eq. I:

x + 5 = (2/3)(y + 5) Eq. I

x - 3 = (1/2 )(y -3) Eq. II

x + 5 = (2/3)y + 10/3

-[x - 3 = (1/2)y - 3/2)]

x - x + 5 + 3 = (2/3)y - (1/2)y + 10/3 + 3/2

8 = (2/3)y - (1/2)y + 10/3 + 3/2

8 = (4/6)y - (3/6)y + 20/6 + 9/6

8 = (1/6)y + 29/6

6(8) = 6[(1/6)y + 29/6)]

48 = y + 29

48 - 29 = y

19 = y

Use Eq. II and the value for y to solve for x:

x + 5 = (2/3)(y + 5) Eq. I

x + 5 = (2/3)(19 + 5) substitute 19 for y

x + 5 = (2/3)(24)

x + 5 = 16

x = 16 - 5

x = 11

Check your answers by solving each equation with x = 11 and y = 19. I'll leave this for you.