Answer:
The answer choices are garbled, thus you cannot pick among them. Below, you can see how to determine this system:
Explanation:
<u>1. Name your variables:</u>
<u>2. He sells the shorts for $12</u>
Then, the value of s shorts is represented by:
<u>3. He sells the T-shirts for $5 each. </u>
Then, the value of t Tshirts is:
<u>4. Total value = value of shorts + value of T-shirts:</u>
- Value of sales = 12s + 5t
<u>5. It takes him 30 minutes to design a T-shirt.</u>
Then, using 30 minutes = 0.5 hours, the time to design t Tshirts is:
<u>6. It takes him an hour and 30 minutes to desing a pair of shorts</u>
Then, using an hour and 30 minutes = 1.5 hours, the time to desing s pairs of shorts is:
<u>7. Greg can work 15 hours a day, at most.</u>
Then, the total time must be equal or less than 15 hours:
- 0.5t + 1.5s ≤ 15 ↔ first inequality
<u>8. He must design at least 10 items each day, </u>
Then, the total number of items is equal to or greater than 10:
- t + s ≥ 10 ↔ second inequality
<u>9. He cannot design more than 25 items in one day. </u>
Then, the total number of items is equal to or less than 25:
- t + s ≤ 25 ↔ third inequality
<u>10. You must add the natural constraints: the items cannot be negative:</u>
Summarizing the inequalities are:
Divide the first inequality by 1.5:
And the five inequalities can be written as: