Question

short response questions (5 questions)
answer the questions below using the provided textboux.
question 1
write an equation in the form ( y = m x + b ) for each person that shows
how many total meals they will have packed after ( x ) hours.
carlos ( y = 4 x + 10 ).
maya ( y = 2 x + 16 )
question 2
use substitution to solve the system of equations you wrote in
question 1. show your steps, and find out after how many hours they
will have packed the same number of meals.
question 3
what does your solution from question 2 mean in this situation?

Explanation:

Step1: Set the two equations equal

Since \(y = 4x + 10\) (Carlos) and \(y=2x + 16\) (Maya), we set \(4x + 10=2x + 16\).

Step2: Solve for \(x\)

Subtract \(2x\) from both sides: \(4x-2x + 10=2x-2x + 16\), which simplifies to \(2x+10 = 16\).
Then subtract \(10\) from both sides: \(2x+10 - 10=16 - 10\), so \(2x=6\).
Divide both sides by \(2\): \(x=\frac{6}{2}=3\).

Answer:

After \(3\) hours, Carlos and Maya will have packed the same number of meals.