Question

Seiji and Gavin both worked hard over the summer. Together they earned a total of $525. Gavin earned $25 more than Seiji. Write a system of equations for the situation. Use s for the amount Seiji earned and g for the amount Gavin earned. Graph the equations of the system on the graph provided on the next page. Note: Insert->Shape will allow you to add lines, draw dots, and otherwise insert shapes in both Microsoft Word and LibreOffice. The graph should be big enough for you to easily plot points using this method. If you do not want to graph using the drawing tools built into Microsoft Word or LibreOffice you may also print out, graph by hand, and scan the page. Please note it’s perfectly okay to upload multiple files. Use your graph to estimate how much each person earned, and explain your results.
THERE ARE THREE PARTS TO THIS PLEASE ANSWER ALL 3 100% CORRECTLY AND SHOW YOUR WORK IF NOT YOU WILL BE REPORTED

Answer 1

Answer:

Part 1) see the explanation

Part 2) The graph in the attached figure

Part 3) The  amount earned by Seiji was $250 and the amount earned by Gavin was $275

Step-by-step explanation:

Part 1) Let

s ----> amount earned by Seiji

g ----> amount earned by Gavin

we know that

$s+g=525$ -----> equation A

$g=s+25$ ----> equation B

Part 2) Graph the equations of the system

To graph the lines find out the intercepts

Remember that

The x-intercept is the value of x when the value of y is equal to zero

The y-intercept is the value of y when the value of x is equal to zero

In this problem the s-axis represent the x-axis and the g-axis represent the y-axis

Equation A

Find the s-intercept

For g=0

$s+0=525$ ----> $s=525$

The s-intercept is the point (525,0)

Find the g-intercept

For s=0

$0+g=525$ ----> $g=525$

The g-intercept is the point (0,525)

To graph the line A plot the intercepts and join the points

Equation B

Find the s-intercept

For g=0

$0=s+25$  ----> $s=-25$

The s-intercept is the point (-25,0)

Find the g-intercept

For s=0

$g=0+25$  ----> $g=25$

The g-intercept is the point (0,25)

To graph the line B plot the intercepts and join the points

using a graphing tool

Plot the intercepts both lines and join the points

see the attached figure

Part 3) we know that

The solution of the system of equations is the intersection point both graphs

The solution is the point (250,275)

see the attached figure

therefore

The  amount earned by Seiji was $250 and the amount earned by Gavin was $275