Question

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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?

Explanation:

Step1: Define system of equations

From the problem:

1. Sum of ages: $s + j = 70$
2. Sharon's age relation: $s = 4j$

Step2: Solve the system

Substitute $s=4j$ into $s+j=70$:
$4j + j = 70$
$5j = 70$
$j = 14$
Then $s = 4(14) = 56$
Solution: $(s,j)=(56,14)$

Step3: Verify graph conditions

• For $s+j=70$, the intercepts are $(s=70,j=0)$ and $(s=0,j=70)$
• For $s=4j$, it is a line through the origin with slope 4, passing through $(56,14)$
• The correct graph will have these two lines intersecting at $(56,14)$ (s-axis=56, j-axis=14), which matches the top graph (first option, with the intersection at s=56, j=14, and the sum line connecting (70,0) to (0,70)).

Answer:

The top graph (first option, with the intersection point at Sharon's age = 56, John's age = 14, and the two lines: one connecting (70,0) to (0,70), the other passing from the origin to (56,14)) is the correct representation.