Question

Grayson needs to earn at least $1,000 in order to pay for his summer vacation. He works two different jobs. His tutoring job pays $20 per hour, while working as a cashier pays $8 per hour. He cannot work more than 300 hours total before his vacation. Write the system of linear inequalities that models this situation. Let x represent the number of hours he works as a tutor, and let y represent the number of hours he works as a cashier.(1 point) Responses x+y≤300 and 20x+8y≤1,000 x plus y less-than-or-equal-to 300 and 20 x plus 8 y less-than-or-equal-to 1,000 x+y≤300 and 20x+8y≥1,000 x plus y less-than-or-equal-to 300 and 20 x plus 8 y greater-than-or-equal-to 1,000 x+y≥1,000 and 20x+8y≤300 x plus y greater-than-or-equal-to 1,000 and 20 x plus 8 y less-than-or-equal-to 300 x+y≤300 and x+y≥1,000 x plus y less-than-or-equal-to 300 and x plus y greater-than-or-equal-to 1,000 Skip to navigation

Answer 1

To formulate the system of linear inequalities based on Grayson's situation, we define:

- \( x \): the number of hours he works as a tutor
- \( y \): the number of hours he works as a cashier

We have the following conditions:

1. **Total hours worked constraint**: He cannot work more than 300 hours in total.
\[
x + y \leq 300
\]

2. **Minimum earnings requirement**: He needs to earn at least $1,000. The earnings from tutoring is $20 per hour and from cashier work is $8 per hour.
\[
20x + 8y \geq 1,000
\]

Putting these conditions together, we have the system of inequalities:
\[
\begin{align*}
x + y & \leq 300 \\
20x + 8y & \geq 1,000
\end{align*}
\]

Thus, the correct option is:
\( x + y \leq 300 \) and \( 20x + 8y \geq 1,000 \)