Jenny and Bill have a combined age of 50. Sixteen years ago Jenny was twice as old as Bill. Let Jenny be x years and Billy y years

Answer 1

We can set up a system of equations based on the information given. Let's define:

• \( x \) = Jenny's current age
• \( y \) = Bill's current age

From the problem, we have the following two equations:

1. The combined age:
   \[ x + y = 50 \]

2. The age difference from sixteen years ago:
   Sixteen years ago, Jenny's age was \( x - 16 \) and Bill's age was \( y - 16 \). It is given that at that time, Jenny was twice as old as Bill: \[ x - 16 = 2(y - 16) \]

Now, we can simplify the second equation:

\[ x - 16 = 2y - 32 \] \[ x = 2y - 32 + 16 \] \[ x = 2y - 16 \]

Now we have a system of two equations:

1. \( x + y = 50 \)
2. \( x = 2y - 16 \)

We can substitute the second equation into the first equation:

\[ (2y - 16) + y = 50 \] \[ 3y - 16 = 50 \] \[ 3y = 66 \] \[ y = 22 \]

Now that we have \( y \), we can find \( x \) using the first equation:

\[ x + 22 = 50 \] \[ x = 50 - 22 \] \[ x = 28 \]

Thus, Jenny's current age is \( 28 \) and Bill's current age is \( 22 \).

To summarize:

• Jenny's age, \( x = 28 \)
• Bill's age, \( y = 22 \)

You can check the conditions:

• Combined age: \( 28 + 22 = 50 \) (correct)
• Sixteen years ago, Jenny was \( 28 - 16 = 12 \) and Bill was \( 22 - 16 = 6 \). Indeed, \( 12 \) is twice \( 6 \) (correct).

So the solution is verified.