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.

Question

UpStudy AI · Accepted Answer

Let's analyze each statement based on the given system of equations:

$$
\left\{\begin{array}{c}
x + y = 90 \
5x + 8y = 600
\end{array}\right.
$$

Here:
- $$ x $$ represents the number of hours Pat spends babysitting.
- $$ y $$ represents the number of hours Pat spends mowing lawns.
- $$ 5x $$ is the money earned from babysitting.
- $$ 8y $$ is the money earned from mowing lawns.
- $$ 600 $$ is the total money earned in that month.

Now, let's evaluate each statement:

**(A) The variable $$ y $$ represents the number of lawns Pat mows.**

- **Incorrect.** $$ y $$ represents the number of hours Pat spends mowing lawns, not the number of lawns mowed.

**(B) The variable $$ x $$ represents the number of lawns Pat mows.**

- **Incorrect.** $$ x $$ represents the number of hours Pat spends babysitting.

**(C) The term $$ 8y $$ represents the amount of money Pat makes babysitting.**

- **Incorrect.** $$ 8y $$ represents the money earned from mowing lawns, not babysitting.

**(D) The term $$ 8y $$ represents the amount of money Pat makes mowing lawns.**

- **Correct.** $$ 8y $$ is the money earned from mowing lawns at \$8 per hour.

**(E) The number 600 represents the total amount of money Pat earned in that month.**

- **Correct.** The equation $$ 5x + 8y = 600 $$ shows that Pat earned a total of \$600.

**Additional Statement:**

**Pat earns \$600 from babysitting 40 hours and mowing lawns for 50 hours.**

- **Correct.** If $$ x = 40 $$ and $$ y = 50 $$, then:
  $$
  5(40) + 8(50) = 200 + 400 = 600
  $$
  This satisfies both equations $$ x + y = 90 $$ and $$ 5x + 8y = 600 $$.

**Summary of Correct Statements:**
- **(D)**
- **(E)**
- **Pat earns \$600 from babysitting 40 hours and mowing lawns for 50 hours.**
The correct statements are: - (D) The term $$ 8y $$ represents the amount of money Pat makes mowing lawns. - (E) The number 600 represents the total amount of money Pat earned in that month. - Pat earns \$600 from babysitting 40 hours and mowing lawns for 50 hours. So, the correct choices are D, E, and the additional statement about Pat's earnings.

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