Both Kayla's spending and Kerri's spending are modeled with nonlinear functions. 8. Pat earns money during the summer by babysitting and mowing lawns. Pat earns \( \$ 5 \) per hour of babysitting and \( \$ 8 \) per hour of mowing lawns. One month last summer Pat worked a total of 90 hours between the two jobs. The system of equations shown can be used to represent this situation. \[ \left\{\begin{array}{c} x+y=90 \\ 5 x+8 y=600 \end{array}\right. \] Which of the following statements are correct? Select all that apply. (A) The variable \( y \) represents the number of lawns Pat mows. (B) The variable x represents the number of lawns Pat mows. (C) The term \( 8 y \) represents the amount of money Pat makes babysitting. (D) The term \( 8 y \) represents the amount of money Pat makes mowing lawns. (E) The number 600 represents the total amount of money Pat earned in that month. (A) Pat earns \( \$ 600 \) from babysitting 40 hours and mowing lawns for 50 hours.
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Pat's work situation is a classic example of a system of linear equations used to model real-life scenarios. When we analyze the equations, it becomes clear that \( x \) stands for the hours spent babysitting and \( y \) represents the hours spent mowing lawns. This way of modeling helps in balancing different activities, showing just how versatile and useful algebra can be in everyday life! In terms of solving the equations, it's a common pitfall to misinterpret the variables. Remember, if you start with the equation \( 5x + 8y = 600 \), you need to clearly define what each variable stands for before diving into calculations. Don’t forget to check your work! A simple mistake in defining \( x \) and \( y \) could lead you to an incorrect conclusion about Pat's earnings.
