Kathy is y years old
Find her age,if 1/2 of wat she was 3 years ago is equal to 1/3 of what she will be in 4 years time
Kathy's age now ---- x
her age 3 years ago -- x-3
her age 4 years from now -- x+4
(1/2)(x-3) = (1/3)(x+4)
times 6
3(x-3) = 2(x+4)
finish it up
3x-9=2x+8,put the like terms together...therefore 3x-2x=8+9 which equals to...x=17 so Kathy's age now is 17 years old....
Let's break down the problem into steps:
Step 1: Define the unknown variable:
Let's assume Kathy's current age is represented by the variable "y".
Step 2: Determine Kathy's age 3 years ago:
Kathy's age 3 years ago would be y - 3.
Step 3: Calculate half of Kathy's age 3 years ago:
Half of Kathy's age 3 years ago is (1/2)(y - 3).
Step 4: Determine Kathy's age in 4 years time:
Kathy's age in 4 years will be y + 4.
Step 5: Calculate one-third of Kathy's age in 4 years time:
One-third of Kathy's age in 4 years time is (1/3)(y + 4).
Step 6: Set up the equation and solve for y:
We are given that half of Kathy's age 3 years ago is equal to one-third of Kathy's age in 4 years time. So we can set up the equation:
(1/2)(y - 3) = (1/3)(y + 4).
To solve this equation, we can multiply both sides by 6 to eliminate the fractions:
6*(1/2)(y - 3) = 6*(1/3)(y + 4).
3(y - 3) = 2(y + 4).
Expanding the equation:
3y - 9 = 2y + 8.
Simplifying the equation:
3y - 2y = 8 + 9.
y = 17.
Therefore, Kathy is 17 years old.
To solve this problem, we need to set up an equation based on the given information and then solve for Kathy's age.
Let's break down the problem step by step:
1. Let's assume Kathy's current age is y years old.
2. "1/2 of what she was 3 years ago" can be written as (1/2)(y-3).
3. "1/3 of what she will be in 4 years time" can be written as (1/3)(y+4).
4. According to the problem, "(1/2)(y-3) is equal to (1/3)(y+4)."
Now, we have the equation:
(1/2)(y-3) = (1/3)(y+4)
To solve for y, we can use cross multiplication:
3(y-3) = 2(y+4)
3y - 9 = 2y + 8
3y - 2y = 8 + 9
y = 17
Therefore, Kathy is 17 years old.