Question

1. Alto and Sheryl both worked hard over the summer. Together they earned a total of $500. Sheryl earned $100 more

than Alto.
(a) Write a system of equations for the situation. Use s for the amount Sheryl earned and a for the amount Alto
earned.

Answer 1

• s + a = 500
• s - a = 100

Explanation:

You want a system of equations that describes the relations, Sheryl and Alto earned $500 with Sheryl earning $100 more than Alto.

(a) Equations

There is an equation associated with each of the numbers. The total earnings can be represented by ...

s + a = 500

The difference in earnings can be represented by ...

s - a = 100

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Additional comment

The solution can be found by adding and subtracting these equations.

(s +a) +(s -a) = (500) +(100) ⇒ 2s = 600 ⇒ s = 300

(s +a) -(s -a) = (500) -(100) ⇒ 2a = 400 ⇒ a = 200

This method of solution works well for all "sum and difference" problems.