Final answer:
To find the number of days until both trees have the same leaf count, set up an equation for each tree's leaf count and solve for the day they equal each other. After setting up and solving the equation, it takes 15 days for both trees to have an equal number of leaves.
Step-by-step explanation:
To determine how many days it will take for both trees to have an equal number of leaves, we have to set up an equation based on the average rates of leaf loss and gain for each tree. Ycela's tree starts with 120 leaves and loses 4.5 leaves per day, while Chelsea's tree starts with 45 leaves and gains 0.5 leaves per day.
The equation representing the leaf count for Ycela's tree after x days is 120 - 4.5x, and for Chelsea's tree, it is 45 + 0.5x. Set these equal to each other to find the point where they have the same number of leaves: 120 - 4.5x = 45 + 0.5x.
Solving for x, we combine like terms to get 75 = 5x, and then divide both sides by 5 to find x = 15. Therefore, it will take 15 days for both trees to have an equal number of leaves.