the movement of the progress bar may be uneven because questions can be worth more or less (including zero)…

the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer. john is 70 years younger than sharon. sharon is 4 times as old as john. if you let s = sharons age and j = johns 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?

the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer. john is 70 years younger than sharon. sharon is 4 times as old as john. if you let s = sharons age and j = johns 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

Explanation:

Step1: Set up the equations

We know that John is 70 years younger than Sharon, so $j=s - 70$. Also, Sharon is 4 times as old as John, so $s = 4j$.

Step2: Substitute one - equation into the other

Substitute $s = 4j$ into $j=s - 70$, we get $j=4j-70$.

Step3: Solve for $j$

Subtract $4j$ from both sides: $j-4j=-70$, which simplifies to $-3j=-70$, then $j=\frac{70}{3}\approx23.33$. Substitute $j$ into $s = 4j$, we get $s=\frac{280}{3}\approx93.33$. The first equation $j=s - 70$ has a slope of 1 and a $y$ - intercept of - 70 (in the $j - s$ plane). The second equation $s = 4j$ or $j=\frac{1}{4}s$ has a slope of $\frac{1}{4}$ and a $y$ - intercept of 0. The solution of the system of equations is the point of intersection of the two lines.

We need to analyze the graphs based on the slopes and intercepts of the two lines. The line $j=s - 70$ has a positive slope of 1 and crosses the $j$ - axis at - 70. The line $j=\frac{1}{4}s$ has a positive slope of $\frac{1}{4}$ and crosses the origin. The correct graph will have two lines intersecting at the point $(s,j)$ where $s\approx93.33$ and $j\approx23.33$.

Since we don't have the option values written out explicitly, we can't give a letter - based answer. But the process to find the correct graph is as above.

If we assume we are looking for the graph where the lines $j=s - 70$ (a line with slope 1 and $j$ - intercept of - 70) and $j=\frac{1}{4}s$ (a line with slope $\frac{1}{4}$ and $j$ - intercept of 0) intersect at the correct point.

We first rewrite the first equation in slope - intercept form $j=s - 70$ and the second as $j=\frac{1}{4}s$. The intersection point of the two lines can be found by solving the system $\begin{cases}j=s - 70\j=\frac{1}{4}s\end{cases}$ as shown above.

Answer:

We need to find the graph where the line $j=s - 70$ (with slope 1 and $j$ - intercept of - 70) and the line $j=\frac{1}{4}s$ (with slope $\frac{1}{4}$ and $j$ - intercept of 0) intersect at the point $(\frac{280}{3},\frac{70}{3})$