Tanya`s grandfather was 8 times older to her 16years ago.He would be 3 times of her age 8 years from now.Eight years ago,what was the ratio of tanya`s age to that of her grand father?
ages now: t and g
16 years ago, (g-16) = 8(t-16)
8 years from now, (g+8) = 3(t+8)
Hmmm. solving those two equation, I don't get integer solutions. That's ok, but unusual. If I have gotten something wrong, fix it and follow through, finishing with the ratio
(t-8)/(g-8)
I get 11/53 with what I wrote
how u got 11/53?
To solve this question, let's break it down step by step:
Step 1: Let's represent Tanya's current age as T and her grandfather's current age as G.
Step 2: According to the first statement, Tanya's grandfather was 8 times older than her 16 years ago. This can be written as:
G - 16 = 8 * (T - 16)
Step 3: According to the second statement, Tanya's grandfather would be 3 times her age 8 years from now. This can be written as:
G + 8 = 3 * (T + 8)
Step 4: Now, we have a system of two equations with two variables. We can solve this system of equations to find the values of T and G.
Solving the equations, we get:
G = 152 - 4T
Step 5: To find the ratio of Tanya's age to her grandfather's age eight years ago, we need to calculate their ages eight years ago.
Let's calculate Tanya's age eight years ago:
T - 8 = (T - 16) - 8
T - 8 = T - 24
T = 16
Now, let's calculate Tanya's grandfather's age eight years ago:
G - 8 = (152 - 4T) - 8
G - 8 = 152 - 4T - 8
G - 8 = 144 - 4T
G = 152 - 4T + 8
G = 160 - 4T
Substituting T = 16:
G = 160 - 4(16)
G = 160 - 64
G = 96
So, Tanya's age eight years ago was 16, and her grandfather's age eight years ago was 96.
Step 6: Now, we can find the ratio of Tanya's age to her grandfather's age eight years ago:
Ratio = Tanya's age / Grandfather's age
Ratio = 16 / 96
Ratio = 1/6
Therefore, the ratio of Tanya's age to her grandfather's age eight years ago was 1:6.