Question

HELP PLEASE Sam and George both worked hard over the summer. Together they earned a total of $525. George earned $75 more than Sam.

a. Write a system of equations for the situation. Use s for the amount Sam earned and g for the amount George earned. b. Graph the equations in the system. Be sure to label all axes and show your scale.
c. Use your graph to determine how much each person earned.

Answer 1

Answer: Sam = $225 George = $300

Explanation:

NOTES:

Sam: s

George: g = s + 75

Together: s + g = 525

a.

The two equations that can be created are "George" and Together"

The system is:
`\left \{ {{\text{g = s + 75}} \atop {\text{s + g = 525}}} \right.`

b.

see attached graph

c.

The intersection of the two lines is at (225, 300). Since Sam represented the x-axis and Georege represented the y-axis, then Sam = $225 and George = $300.

BONUS:

This system can also be solved algebraically using the substitution method.

Replace "g" with "s + 75" into the second equation:

s + (s + 75) = 525

2s + 75 = 525

2s = 450

s = 225

Next, input the s-value into the George equation to solve for g:

g = s + 75 = (225) + 75 = 300