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 \( 20x + 8y \geq 1,000 \)