One year ago Liz was 3 times as old as her brother Jack. In two years she'll only be twice as old as Jack. How old are Liz and Jack now?
To solve this problem, let's set up equations based on the given information.
Let's assume that Liz's current age is "L" and Jack's current age is "J".
We are given two important pieces of information:
1) One year ago, Liz was 3 times as old as Jack. This can be represented as:
L - 1 = 3(J - 1)
2) In two years, Liz will only be twice as old as Jack. This can be represented as:
L + 2 = 2(J + 2)
Now we have a system of two equations with two variables. We can solve this system of equations using algebraic methods.
First, let's solve equation (1) for L:
L - 1 = 3J - 3
L = 3J - 2
Now substitute this value of L in equation (2):
3J - 2 + 2 = 2(J + 2)
3J = 2J + 4
3J - 2J = 4
J = 4
Now substitute the value of J back into equation (1):
L = 3(4) - 2
L = 12 - 2
L = 10
Therefore, Liz is currently 10 years old and Jack is currently 4 years old.
L - 1 = 3(J - 1)
L + 2 = 2(J +2) = 2J + 4
L = 2J + 2
Substitute 2J + 2 for L in the first equation and solve for J. Insert that value into the last equation to solve for L. Check by putting both values into the first equation.