Question: Part 1 of 3 Elijah and Aubrey have summer jobs. Elijah deposits the same amount of money in…

Part 1 of 3

Elijah and Aubrey have summer jobs. Elijah deposits the same amount of money in his account every week. The equation \( y = 125x + 72 \) represents his bank balance any given week of the summer. Aubrey also deposits the same amount into her account every week. At the end of the third week she has $338. At the end of the sixth week she has $773. Complete parts a to c below.

a. Write an equation to represent Aubrey’s bank balance any given week of the summer.

(Simplify your answer. Type an equation. Type your answer in slope-intercept form. Use integers or decimals for any numbers in the equation.)

Solution

Elijah and Aubrey have summer jobs. Elijah deposits the same amount of money in his account every week. The equation \( y = 125x + 72 \) represents his bank balance any given week of the summer. Aubrey also deposits the same amount into her account every week. At the end of the third week, she has $388. At the end of the sixth week, she has $773. a. Write an equation to represent Aubrey’s bank balance any given week of the summer. To find the equation representing Aubrey’s bank balance, we need to determine the initial amount and the weekly deposit. First, let’s identify two points from the information given: After 3 weeks, Aubrey has $388. After 6 weeks, Aubrey has $773. These points can be written as \((3, 388)\) and \((6, 773)\). Next, calculate the slope (rate of change) using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substitute the values: \[ m = \frac{773 - 388}{6 - 3} \] \[ m = \frac{385}{3} = 128.33 \] So, the weekly deposit amount is approximately $128.33. Now, to find the initial amount (\(b\)), use point \((3, 388)\) in the equation \(y = mx + b\): \[ 388 = 128.33 \times 3 + b \] \[ 388 = 384.99 + b \] \[ b = 388 - 384.99 \] \[ b = 3.01 \] Thus, the equation representing Aubrey’s bank balance is: \[ y = 128.33x + 3.01 \]