Question

This year, the ratio of Alan's age to Bernice's age is 1:2. Four years ago, the total age of Alan and Bernice was 55 years. How old is Alan this year?​

Answer 1

By setting up and solving equations, Alan's age this year can be found to be 22.33 years, which can be rounded down to 22.

Step-by-step explanation:

To find Alan's age this year, we can start by setting up an equation using the given ratio. Let's let A represent Alan's age and B represent Bernice's age.

We know that the ratio of Alan's age to Bernice's age is 1:2, which can be written as A:B = 1:2.

Next, we can set up an equation based on the information given four years ago. The total age of Alan and Bernice four years ago was 55 years, which can be written as A-4 + B-4 = 55.

Now, we can solve these two equations simultaneously to find the value of A, which represents Alan's age this year.

Substituting the ratio into the second equation, we get (A-4) + (2A-8) = 55.

Combining like terms, we have 3A - 12 = 55.

Adding 12 to both sides of the equation, we get 3A = 67.

Finally, dividing both sides of the equation by 3, we find that A = 22.33, which we can round down to 22. Therefore, Alan is 22 years old this year.

Answer 2

21 years old

Step-by-step explanation:

Set Alan's age as x, Bernice's age as y

2x=y

x-4+y-4=55

x+y=63

3y=63

x=21

y=42