Question

John is 70
years younger than Sharon. Sharon is 4
times as old as John.

If you let s=
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

To formulate the problem with a system of equations, we can represent the ages of Sharon and John as follows:

1. John is 70 years younger than Sharon:
\[
j = s - 70
\]

2. Sharon is 4 times as old as John:
\[
s = 4j
\]

Now we can rewrite the first equation in terms of \( j \) and substitute it into the second equation:

From the first equation:
\[
s = j + 70
\]

Substituting this expression for \( s \) into the second equation:
\[
j + 70 = 4j
\]

Now we can solve for \( j \):
\[
70 = 4j - j
\]
\[
70 = 3j
\]
\[
j = \frac{70}{3} \approx 23.33
\]

Now substituting \( j \) back into one of the equations to find \( s \):
\[
s = j + 70 \approx 23.33 + 70 \approx 93.33
\]

Thus:
- John's age ( \( j \) ) is approximately 23.33 years.
- Sharon's age ( \( s \) ) is approximately 93.33 years.

To represent this system of equations graphically, you would plot the two equations:
- The line for \( j = s - 70 \) would have a slope of 1 with a y-intercept of -70.
- The line for \( s = 4j \) would have a y-intercept of 0 and a slope of 4.

The intersection of these two lines would represent the solution to the system, which corresponds to \( (j, s) = (23.33, 93.33) \).

While I can't produce images, you can visualize this by plotting both lines on a graph where the x-axis represents John's age and the y-axis represents Sharon's age. The point where the lines intersect is the solution to the problem.