Question

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.