Question

HELP!

3. Jose and Camden both worked hard over the summer. Together, they earned a total of $310. Jose earned $40 more than Camden. How much did each of them earn?

(a) Write a system of two equations with two variables to model this problem.

(b) Use substitution or the elimination method to solve the system.

(c) Graph both equations.

(d) Answer the question.

Answer 1

• a) j+c=310; j-c=40
• b) (j, c) = (175, 135)
• see attached
• Jose earned $175; Camden earned $135

Explanation:

Let j and c represent Jose's and Camden's earnings, respectively.

(a) One equation can be written for the total; another for the difference:

j + c = 310 . . . . their total earnings

j - c = 40 . . . . . the difference in their earnings

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(b) It is convenient to add these two equations to eliminate c:

(j +c) +(j -c) = (310) +(40)

2j = 350

j = 175

Then c can be found as ...

c = j -40 = 175 -40 = 135

The solution is (j, c) = (175, 135).

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(c) Using x for j, and y for c, we can use Desmos to graph the equations. The result is attached.

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(d) Jose earned $175 over the summer; Camden earned $135.