Justin is 3 years older then Sam, and Justin’s age in 2 years will be twice what Sam’s age was 3 years ago. Find their present ages.
i got 14 and 17 but the answer is wrong
J = Justin's age
S = Sam's age
Justin is 3 years older then Sam mean:
J = S + 3
Justin’s age in 2 years will be twice what Sam’s age was 3 years ago mean:
J + 2 = 2 ( S - 3 )
Replace J = S + 3 in this equation.
S + 3 + 2 = 2 * S - 2 * 3
S + 5 = 2 S - 6 Subtract 5 to both sides
S + 5 - 5 = 2 S - 6 - 5
S = 2 S - 11 Add 11 to both sides
S + 11 = 2 S - 11 + 11
S + 11 = 2 S Subtracr S to both sides
S + 11 - S = 2 S - S
11 = S
S = 11 yrs
J = S + 3 = 11 + 3 = 14 yrs
To solve this problem, let's assign variables to Justin's and Sam's present ages. Let's say Justin's age is J and Sam's age is S.
Given that "Justin is 3 years older than Sam," we can write the equation:
J = S + 3 (Equation 1)
Also, given that "Justin’s age in 2 years will be twice what Sam’s age was 3 years ago," we can write the equation:
J + 2 = 2(S - 3) (Equation 2)
Now, we have a system of two equations (Equation 1 and Equation 2) with two variables (J and S). We can solve this system of equations to find their present ages.
Substituting Equation 1 into Equation 2, we have:
(S + 3) + 2 = 2(S - 3)
S + 5 = 2S - 6
11 = S
Now, substitute the value of S back into Equation 1:
J = 11 + 3
J = 14
Therefore, Justin's present age is 14 and Sam's present age is 11.
Let's solve this step-by-step:
Let's assume Sam's age is x.
According to the given information, Justin is 3 years older than Sam, so Justin's age is x + 3.
In 2 years, Justin's age will be x + 3 + 2, and Sam's age 3 years ago was x - 3.
The problem states that in 2 years, Justin's age will be twice what Sam's age was 3 years ago:
So we can write the equation as:
x + 3 + 2 = 2(x - 3)
Now let's solve the equation:
x + 5 = 2x - 6
x - 2x = -6 - 5
-x = -11
Dividing both sides by -1, we get:
x = 11
So, Sam's present age is 11 years old.
Now, to find Justin's age, we can substitute x = 11 into the equation x + 3:
Justin's age = 11 + 3 = 14
Therefore, Sam is 11 years old and Justin is 14 years old.