One half of Heather's age two years from now plus one third of her age three years ago is twenty years. How old is she now?
Let x= Heather's age now
X must be a whole number that is positive.
(1/2)(x+2) + (1/3)(x-3) = 20
multiply both sides by six
3(x+2) + 2(x-3) = 120
5 x = 120
x = 24
Ohhhh thank you so much!!
Let's solve the equation step by step.
Step 1: Translate the given information into an equation.
"One half of Heather's age two years from now" can be written as (1/2)(x + 2).
"One third of her age three years ago" can be written as (1/3)(x - 3).
The equation can be written as:
(1/2)(x + 2) + (1/3)(x - 3) = 20
Step 2: Simplify the equation.
Multiplying each term by 6 to eliminate the denominators, we get:
3(x + 2) + 2(x - 3) = 120
Simplifying further, we get:
3x + 6 + 2x - 6 = 120
5x = 120
x = 24
Step 3: Verify the solution.
Plug the value of x back into the original equation:
(1/2)(24 + 2) + (1/3)(24 - 3) = 20
12 + 5 = 20
Since the equation is true, the solution x = 24 is correct.
Therefore, Heather is 24 years old now.
To solve this problem, we need to break it down into smaller steps.
Step 1: Define the variables.
Let x be Heather's age now.
Step 2: Formulate the equation based on the given information.
According to the problem, one-half of Heather's age two years from now plus one-third of her age three years ago is twenty years. Mathematically, we can write this as:
(1/2)(x + 2) + (1/3)(x - 3) = 20
Step 3: Simplify the equation.
To simplify the equation, we need to distribute the fractions and combine like terms.
(1/2)x + 1 + (1/3)x - 1 = 20
Combining like terms, we have:
(5/6)x = 20
Multiply both sides by 6/5 to isolate x:
x = (20 * 6) / 5
x = 24
Step 4: Interpret the answer.
Therefore, Heather is currently 24 years old.