Al is twice as old as Bill, who is twice as old as Carl. In 10 years, Al will be twice as old as Carl. How old is Al now?
A. 40
B. 20
C. 10
D. 5
I usually start with the smallest quantity, which here is Carl's age
let Carl's age be x
then Bill is 2x
and Al is 4x
in 10 years:
Carl --- x+10
Bill --- 2x+10
Al ---- 4x + 10
so 4x+10 = 2(x+10)
4x + 10 = 2x + 20
2x = 10
x = 5
So now Al is 4(5) = 20
check:
present ages:
Carl -- 5
Bill --- 10
Al ---- 20
10 years from now:
Al will be 30 and Carl will be 15
Is Al twice as old as Carl ?? YES
thanks
Let's solve this problem step by step.
1. Let's assume Carl's age as x.
2. According to the problem, Bill is twice as old as Carl, so Bill's age would be 2x.
3. Al is twice as old as Bill, so Al's age would be 2 * 2x = 4x.
4. In 10 years, Al will be 4x + 10 years old, and Carl will be x + 10 years old.
5. According to the problem, in 10 years, Al will be twice as old as Carl, so we can set up the equation: 4x + 10 = 2(x + 10).
6. Solve the equation: 4x + 10 = 2x + 20
- Subtract 2x from both sides: 4x - 2x + 10 = 2x - 2x + 20
- Simplify: 2x + 10 = 20
- Subtract 10 from both sides: 2x + 10 - 10 = 20 - 10
- Simplify: 2x = 10
- Divide by 2: 2x / 2 = 10 / 2
- Simplify: x = 5
7. Carl is 5 years old.
8. Bill is 2x = 2 * 5 = 10 years old.
9. Al is 4x = 4 * 5 = 20 years old.
Therefore, Al is currently 20 years old.
So the answer is B, 20.
To solve this problem, we can start by assigning variables to the ages of Al, Bill, and Carl.
Let's say Al's age is A, Bill's age is B, and Carl's age is C.
According to the first sentence, "Al is twice as old as Bill," we can write the equation A = 2B.
Similarly, the second sentence states that "Bill is twice as old as Carl," so the equation for this relationship is B = 2C.
The third sentence provides additional information. In 10 years, Al will be twice as old as Carl. So, we can write the equation A + 10 = 2(C + 10).
Now, we can substitute the value of B from the first equation into the second equation to replace B in terms of C. It becomes 2C = 2C.
Next, we substitute the value of B from the second equation into the third equation to replace B and simplify it. We get A + 10 = 2C + 20.
Now, let's solve this equation to find the value of A.
By rearranging the equation, we have A = 2C + 10.
Since we have two equations for A in terms of C, we can now set them equal to each other:
A = 2B and A = 2C + 10.
Substituting 2B for A in the second equation, we get 2B = 2C + 10.
Now, we can substitute the value of B in terms of C using B = 2C:
2(2C) = 2C + 10.
Simplifying the equation, we get 4C = 2C + 10.
Subtracting 2C from both sides, we have 2C = 10.
Dividing both sides of the equation by 2, we find C = 5.
Now, substitute the value of C into either equation to find A:
A = 2C + 10 = 2(5) + 10 = 20.
So, Al is currently 20 years old.
Therefore, the answer is B. 20 years old.