Answer:
(a) [tex]s+g=525\\g=s+25[/tex]
(b) The graph is shown below.
(c) Seiji earned $ 250 and Gavin earned $ 275.
Step-by-step explanation:
Given:
Sum of earnings of Seiji and Gavin = $ 525
Gavin earns $ 25 more that that of Seiji.
(a)
So, as per question, if [tex]s[/tex] and [tex]g[/tex] are the amounts earned by Seiji and Gavin respectively, then;
[tex]s+g=525\\g=s+25[/tex]
(b)
The graph is plotted using the x and y intercepts of each line.
For the line, [tex]s+g=525[/tex], the x intercept is at [tex]g=0[/tex]. So, x intercept is (525,0). Similarly, the y intercept is when [tex]s=0[/tex], which is (0,525). Draw a line passing through these two points. The blue line represents [tex]s+g=525[/tex].
We follow the same process to plot the next line. The x intercept is at (-25,0) and y intercept is at (0,25). Draw a line passing through these two points. The green line represents [tex]g=s+25[/tex].
The graph is shown below.
(c) From the graph, the point of intersection of the two lines gives the earnings of each of the persons.
The [tex]x[/tex] value of the point of intersection is the earning of Seiji which is $ 250 and the [tex]y[/tex] value is the earning of Gavin which is $ 275 as shown in the graph.
We can find the same algebraically also.
Substituting the value of [tex]g[/tex] in the first equation, we get
[tex]s+s+25=525\\2s+25=525\\2s=525-25\\2s=500\\s=\frac{500}{2}=\$\ 250[/tex]
Now, [tex]g=s+25=250+25=\$\ 275[/tex]
Therefore, algebraically, Seiji earned $ 250 and Gavin earned $ 275.
