Your cousin is eight years older than your brother three years ago your cousin was twice as old as your brother how old is your cousin now how old is your brother now
Present Past
Cousin x+8 2(x-3)
Brother x x-3
Solution: x+8-3=2(x-3)
x+5 =2x-6
5+6 =2x-x
11 =x (brother)
19 =11+8 (cousin)
Let's break down the problem step by step.
1. Let's assign variables to the ages of your cousin and your brother:
- Cousin's age now: C
- Brother's age now: B
2. Three years ago, your cousin was 8 years older than your brother:
- Cousin's age three years ago: C - 3
- Brother's age three years ago: B - 3
3. According to the problem, your cousin was twice as old as your brother three years ago:
- C - 3 = 2 * (B - 3)
4. Simplify the equation:
- C - 3 = 2B - 6
5. Move all terms involving C to one side of the equation and all terms involving B to the other side:
- C - 2B = -3
6. Since we have only one equation, we cannot solve for both C and B separately. However, we can express one variable in terms of the other.
7. Let's solve the equation for C in terms of B:
- C = 2B - 3
So, your cousin's age now is 2 times your brother's age minus 3. The current ages of your cousin and brother cannot be determined without additional information about either of their ages.
To find the current ages of your cousin and brother, we need to break down the information given in the question into equations.
Let's assign variables:
- Let C be the current age of your cousin.
- Let B be the current age of your brother.
From the information provided, we gather two key pieces of information:
1. "Your cousin is eight years older than your brother."
This translates to the equation: C = B + 8.
2. "Three years ago, your cousin was twice as old as your brother."
Three years ago, your cousin's age was C - 3, and your brother's age was B - 3.
This gives us the equation: C - 3 = 2 * (B - 3).
Now we have a system of two equations:
Equation 1: C = B + 8
Equation 2: C - 3 = 2 * (B - 3)
To solve this system, substitute Equation 1 into Equation 2:
(B + 8) - 3 = 2 * (B - 3)
B + 5 = 2B - 6
Simplify the equation:
B - 2B = -6 - 5
-B = -11
Multiply both sides by -1 to isolate B:
B = 11
Now, substitute the value of B back into Equation 1 to find C:
C = B + 8
C = 11 + 8
C = 19
Therefore, your cousin is currently 19 years old, and your brother is currently 11 years old.
Let B = brother's age
and C = cousins agae
====================
B+8 = C
2(B-3) = C-3
Solve those two equations simultaneously for B and C.