the sum of sharons and johns ages is 70. sharon is 4 times as old as john. if you let s = sharons age and j…

the sum of sharons and johns ages is 70. 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 sum of sharons and johns ages is 70. 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 have $s + j=70$ (sum of ages) and $s = 4j$ (Sharon's age relation to John's).

Step2: Substitute $s = 4j$ into $s + j=70$

$4j+j=70$, which simplifies to $5j = 70$.

Step3: Solve for $j$

$j=\frac{70}{5}=14$.

Step4: Solve for $s$

Substitute $j = 14$ into $s = 4j$, so $s=4\times14 = 56$. The solution of the system is the point $(s,j)=(56,14)$. To graph $s + j=70$, we can rewrite it as $j=-s + 70$ (a line with y - intercept 70 and slope - 1). The line $s = 4j$ or $j=\frac{1}{4}s$ has a y - intercept of 0 and a slope of $\frac{1}{4}$. The two lines should intersect at the point $(56,14)$.

We cannot directly choose the correct graph from the description provided in the text, but we know the intersection point of the two lines representing the system of equations should be at $(s = 56,j = 14)$.

Answer:

The graph where the two lines representing $s + j=70$ and $s = 4j$ intersect at the point $(56,14)$ (no specific graph option is labeled in the answer as the graphs are not described by letter or other identifier in the problem statement).