the sum of sharons and johns ages is 70. john is 4 times as old as sharon. if you let s = sharons age and j…
the sum of sharons and johns ages is 70. john is 4 times as old as sharon. 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 the sum of their ages is 70, so $s + j=70$, which can be rewritten as $j = 70 - s$. Also, John is 4 times as old as Sharon, so $j = 4s$.
Step2: Find the solution of the system
Set the two - equations equal to each other: $4s=70 - s$. Add $s$ to both sides: $4s + s=70$, so $5s = 70$. Then $s=\frac{70}{5}=14$. Substitute $s = 14$ into $j = 4s$, we get $j=4\times14 = 56$. The solution of the system $(s,j)=(14,56)$. For the line $j = 70 - s$, when $s = 0$, $j = 70$ and when $j = 0$, $s = 70$. For the line $j = 4s$, when $s = 0$, $j = 0$ and it has a slope of 4. The two lines should intersect at the point $(14,56)$. We need to visually check which graph has the lines $j = 70 - s$ (a line with y - intercept 70 and slope - 1) and $j = 4s$ (a line with y - intercept 0 and slope 4) intersecting at $(14,56)$.
Answer:
(Without seeing the actual options clearly, we can't pick a specific option. But the correct graph should have two lines: one with the equation $j = 70 - s$ and another with the equation $j = 4s$ intersecting at the point $(14,56)$)