5 years from now a boy's age will be 2 time the square of what it was 5 years ago.how old is he now?
a)15/2 years c)7 years
b)3 years d) 8 years
age now: x
age in 5 years: x+5
age 5 years ago: x-5
so, write the words in math
x+5 = 2(x-5)^2
now just solve for x. Since you have a quadratic function, you will get two answers. Only one answer will make sense.
Now: X years old.
5 yrs. ago: x-5 yrs. old.
5 yrs. from now: x+5 years old.
x+5 = 2*(x-5)^2.
x+5 = 2(x^2-10x+25).
x+5 = 2x^2-20x+50,
-45 = 2x^2-21x,
2x^2-21x+45 = 0.
Use Quadratic Formula:
X = (21 +- sqrt(441-360))/4 = 30/4 = 15/2, and 3.
Use the larger number:
X = 15/2 = 7.5 Years old.
Let's assume the boy's current age is x years.
According to the information given, 5 years from now, the boy's age will be (x + 5) years.
And 5 years ago, the boy's age was (x - 5) years.
According to the question, 5 years from now, the boy's age will be 2 times the square of what it was 5 years ago. Mathematically, we can represent this as:
(x + 5) = 2 * (x - 5)^2
Simplifying this equation step by step:
(x + 5) = 2 * (x^2 - 10x + 25)
x + 5 = 2x^2 - 20x + 50
0 = 2x^2 - x - 45
Now we can solve this quadratic equation by factoring or using the quadratic formula. Factoring is preferable in this case.
0 = (2x + 9)(x - 5)
Setting each factor equal to zero:
2x + 9 = 0 or x - 5 = 0
Solving each equation:
2x = -9 or x = 5
Dividing both sides by 2 in the first equation:
x = -9/2 or x = 5
Since the age of a person cannot be negative, we can conclude that the boy is currently 5 years old.
Therefore, the correct answer is:
d) 8 years
To find the boy's current age, we can solve the problem algebraically.
Let's denote the boy's current age as "x".
According to the problem, in 5 years from now, the boy's age will be 2 times the square of what it was 5 years ago. So, the equation becomes:
x + 5 = 2 * (x-5)^2
To solve this equation, we need to follow these steps:
Step 1: Expand the squared term:
x + 5 = 2 * (x^2 - 10x + 25)
Step 2: Distribute the 2 to each term inside the parentheses:
x + 5 = 2x^2 - 20x + 50
Step 3: Rearrange the equation into a quadratic equation and set it equal to zero:
2x^2 - 21x + 45 = 0
Step 4: Solve the quadratic equation by factoring or using the quadratic formula.
However, after solving this quadratic equation, we find that it does not have any real solutions.
Therefore, we cannot determine the boy's current age based on the given information.