One-third of Derick's age two years ago is equal to a quarter of his age four years from now. How old is he now?
Please provide the following:
-Representation
-Equation
-Solution
-Answer
-Checking
Let x = Derick's age now.
(x-2)/3 = (x+4)/4
Solve for x.
4(x-2) = 3(x+4)
x = 12+8 = 20
Two years ago he was 18. 1/3 of that is 6
Four years from now he is 24. 1/4 of that is also 6.
Factorize 2x2square+8x - 10=0
Representation:
Let's represent Derick's current age as "x".
Equation:
1/3 * (x - 2) = 1/4 * (x + 4)
Solution:
To solve this equation, we can start by cross-multiplying:
4 * (x - 2) = 3 * (x + 4)
Expanding the brackets:
4x - 8 = 3x + 12
Bringing all the terms to one side:
4x - 3x = 12 + 8
x = 20
Answer:
Derick is currently 20 years old.
Checking:
To check if our answer is correct, let's substitute the value of x into the original equation:
1/3 * (20 - 2) = 1/4 * (20 + 4)
6 = 6
Since both sides of the equation are equal, our solution of x = 20 is correct.