Tony is 57 years younger than Elizabeth. 9 years ago, Elizabeth's age was 4 times Tony's age. How old is Tony now?
4(t-9) = t+57-9
t = 28
So, Tony is 28 and Elizabeth is 85
9 years ago, they were 19 and 76
76 = 4*19
31
To determine Tony's age, we need to solve this problem step by step. Let's break it down:
Let's assume Tony's current age is "T" and Elizabeth's current age is "E".
We are given that Tony is 57 years younger than Elizabeth, so we can write the first equation as:
T = E - 57
We are also given that 9 years ago, Elizabeth's age was four times Tony's age. So, if we subtract 9 from both Tony's and Elizabeth's current ages, we get:
(E - 9) = 4(T - 9)
Now we have two equations:
1) T = E - 57
2) (E - 9) = 4(T - 9)
To solve this system of equations simultaneously, we can substitute equation 1) into equation 2).
Substituting T = E - 57 into (E - 9) = 4(T - 9), we get:
(E - 9) = 4((E - 57) - 9)
Expanding the equation, we have:
(E - 9) = 4(E - 66)
Expanding further, we get:
E - 9 = 4E - 264
Rearranging the equation, we have:
3E = 255
Now dividing by 3, we find:
E = 85
We know T = E - 57, so:
T = 85 - 57
T = 28
Therefore, Tony is currently 28 years old.
To summarize:
1. Let T represent Tony's age and E represent Elizabeth's age.
2. Set up the equation T = E - 57 to represent Tony being 57 years younger than Elizabeth.
3. Set up the equation (E - 9) = 4(T - 9) to represent Elizabeth's age being four times Tony's age 9 years ago.
4. Substitute the value of T from the first equation into the second equation.
5. Solve the resulting equation to find E = 85.
6. Substitute E = 85 back into the first equation to find T = 28.
7. Therefore, Tony is currently 28 years old.