One year ago Liz was three times as old as her brother Jack. In two years she’ll be only twice as old as Jack. How old are Liz and Jack now?
To solve this problem, let's assign variables to represent the ages of Liz and Jack. Let's call Liz's current age "L" and Jack's current age "J".
From the given information, we can find two equations:
Equation 1: "One year ago Liz was three times as old as her brother Jack" can be represented as (L - 1) = 3(J - 1)
Equation 2: "In two years she’ll be only twice as old as Jack" can be represented as (L + 2) = 2(J + 2)
We now have a system of two equations with two variables. We can solve this system using various methods, such as substitution or elimination.
Let's use substitution to find the values of L and J.
From Equation 1, we can rearrange it as: L = 3(J - 1) + 1
Substituting this value of L into Equation 2, we get:
(3(J - 1) + 1 + 2) = 2(J + 2)
Simplifying the equation: 3J - 3 + 1 + 2 = 2J + 4
Combining like terms: 3J = 2J + 4
Simplifying further: J = 4
Substituting this value of J back into Equation 1, we get: L = 3(4 - 1) + 1 = 12
Therefore, Liz is 12 years old and Jack is 4 years old.
L - 1 = 3 (j-1)
L + 2 =2(j+2)
L = 1+3 j - 3 = 3 j - 2
L = -2 + 2j + 4 = 2 j +2
so
3j-2=2j+2
j = 4 etc etc etc