Final answer:
To determine how many weeks you must babysit to earn enough money to buy the new gaming chair, you can solve the equation 27.5w - 144.99 = 309.99. The value of w is 17, so you need to babysit for 17 weeks.
Step-by-step explanation:
To determine how many weeks, w, you must babysit to earn enough money to buy the new gaming chair, we can write and solve the equation 27.5w - 144.99 = 309.99.
We start with the amount already saved, $144.99, and then calculate the additional amount earned each week babysitting, which is $27.50.
We subtract the total cost of the gaming chair, $309.99, and set it equal to 0. By rearranging the equation and solving for w, we find that w is equal to 17.
This means you need to babysit for 17 weeks to earn enough money to buy the new gaming chair.