Question

1. samantha works twice as many hours per week as adriana. together they work a total of 39 hours in one week.

a) write an equation to represent the information in the first sentence.
b) write an equation to represent the information in the second sentence.

Explanation:

Define variables for the situation

Let \(S\) represent the number of hours Samantha works per week.
Let \(A\) represent the number of hours Adriana works per week.

Translate the first sentence

Using the Linear Modeling knowledge point

$$ S = 2A $$

Translate the second sentence

Using the Systems of Equations knowledge point

$$ S + A = 39 $$

Answer:

Question 3a

\(S = 2A\) (where \(S\) is Samantha's hours and \(A\) is Adriana's hours)

Question 3b

\(S + A = 39\)