1. Sharon and Geordi both worked hard over the summer. Together they eamed a total of $525. Geordi eamed $75 more than Sharon

(a) Write a system of equations for the situation. Use s for the amount Sharon earned and g for the amount
Seardi earned

(b) Graph the equations of the system on the graph provided on the next page.

(c) Use your graph to estimate how much each person earned, and explain your results.

a)

S+G=525

G=S+75

b) See attached pictures

c) S=$225 and G=$300

The point where both graphs meet each other is the point where both equations will be true when having the same S and G values. This is, this is the point where both conditions given by the problem are the same.

Step-by-step explanation:

a) For the first part of the problem, the addition of both amounts will give us the total, so the first equation is:

S+G=525.

On the second equation we need to add 75 to sharon's amount to figure Geordi's amount, so we get:

G=S+75

b) In order to graph the system of equations, we need to find two points for each of the equations. It would be a good idea to solve the first equation for g, so our system of equations would be:

G=525-S

G=S+75

First Equation:

You can pick any value you like for S, for example: S=0 and then substitute it into the equation to get te first G-value:

G=525-0

so G=525.

So the first ordered pair would be (0,525)

You can do the same with a different S-value to get a second point to plot:

S=100

G=525-100

G=424

so the second ordered pair would be (100,424)

and now you can plot the points on the graph and connect them with a straight line.

See attached picture.

Second Equation:

The same procedure is followed for the second equation, in this case I used the same S-values, but you can use different values if you wish, so the two points to plot were:

(0,75)

(100,175)

and the graph looks like the one attached.

c)

In order to figure out how much each person earned, we need to find the point where the two graphs meet each other (see attached picture) in this case the point will be located at (225,300)

This means that Sharon earned a total of $225 while Geordi earned a total of $300.

S=$225 and G=$300

The point where both graphs meet each other is the point where both equations will be true when having the same S and G values. This is, this is the point where both conditions given by the problem are the same.