Question

John is 4
years younger than Sharon. Sharon is s=
times as old as John.

If you let
Sharon's age and j=
John's age, then the problem can be represented by a system of equations. Which of the following shows a graph of this system and the solution to this problem?

Answer 1

Let \( j \) represent John's age and \( s \) represent Sharon's age. According to the problem, we can set up the following equations:

1. \( j = s - 4 \) (John is 4 years younger than Sharon)
2. \( s = k \cdot j \) (Sharon is \( k \) times as old as John)

To express these equations in a standard form suitable for graphing, we can rearrange them:

1. Rearranging \( j = s - 4 \):
\[
s = j + 4
\]

2. Rearranging \( s = k \cdot j \):
\[
s - k \cdot j = 0 \text{ or } s = k j
\]

Now you have the following two equations to graph:

1. \( s = j + 4 \) (Equation for Sharon's age in terms of John's age)
2. \( s = k j \) (Equation for Sharon's age in terms of John's age)

To graph these equations, you would:

- For the first equation \( s = j + 4 \), plot the line with a y-intercept of 4 and a slope of 1. This means that for every 1-year increase in John's age, Sharon's age increases by 1 year.

- For the second equation \( s = k j \), plot the line that passes through the origin (0,0) with a slope of \( k \).

The solution to the system of equations will be where the two lines intersect on the graph.

Without specific values for \( k \), I cannot draw or show a specific graph, but you can plot these lines based on the values you decide for \( k \) and find their intersection point for the solution.

If you have choices for graphs, look for the graph where the lines representing \( s = j + 4 \) and \( s = k j \) intersect, as that point will give you the ages of John and Sharon.