in 2001, lior was four times as old as ezra, and in 2003, lior was twice as old as ezra. how many years older than ezra is lior?
ezra's age in 2001 ----x
lior's age in 2001 ----- 4x
in 2003
ezra --- x+2
lior ----- 4x+2
4x+2 = 2(x+2)
continue ....
why you multiply x+2 by 2?????
To solve this problem, let's set up equations based on the given information.
Let's assume that Lior's age in 2001 is L1, and Ezra's age in 2001 is E1.
According to the given information, "in 2001, Lior was four times as old as Ezra," we can write the equation:
L1 = 4 * E1 -------- Equation 1
Similarly, assuming Lior's age in 2003 is L2 and Ezra's age in 2003 is E2, we have:
L2 = 2 * E2 -------- Equation 2
We need to find the age difference between Lior and Ezra, so we can subtract these equations:
L1 - E1 = 3 * E1 -------------- Equation 3
L2 - E2 = E2 -------------- Equation 4
According to Equation 3, in 2001, Lior was three times older than Ezra.
Using the given information, we can deduce that the age difference remains the same over the years. Therefore, the age difference between Lior and Ezra is always three times Ezra's age.
Hence, Lior is always three years older than Ezra.
To find out how many years older Lior is than Ezra, we first need to determine their ages in 2001 and 2003. Let's use algebra to solve this problem step by step.
Let's assume that Ezra's age in 2001 is x.
Therefore, Lior's age in 2001 will be 4x since Lior was four times as old as Ezra in 2001.
Next, we need to determine their ages in 2003. Two years have passed, so Ezra's age will be x + 2.
Similarly, Lior's age in 2003 will be 2(x + 2) because Lior was twice as old as Ezra in 2003.
Now that we have established their ages in both 2001 and 2003, we can set up an equation to solve for x.
According to the problem, Lior's age in 2001 (4x) is equal to Lior's age in 2003 (2(x + 2)). So we can write:
4x = 2(x + 2)
To solve the equation, we distribute the 2 on the right side:
4x = 2x + 4
Next, subtract 2x from both sides:
4x - 2x = 2x - 2x + 4
Simplifying:
2x = 4
Finally, divide both sides by 2:
2x/2 = 4/2
x = 2
So, in 2001, Ezra was 2 years old.
Now, to find Lior's age in 2001, we substitute x = 2 into the expression 4x:
Lior's age in 2001 = 4(2) = 8 years old.
Thus, Lior is 8 - 2 = 6 years older than Ezra.