Amanda sews T-shirts and sweatshirts to earn money. It costs her $3 to make each T-shirt and $5 to make each sweatshirt. This month she has budgeted $150 for materials for the shirts. It takes Amanda 2 hours to sew a T-shirt and 1 hour to sew a sweatshirt, but because she is booked with other projects for the month she only has 50 hours to sew the shirts.

Which system of inequalities represents this situation, where t represents the number of T-shirts and s represents the number of sweatshirts that Amanda can sew?
{3t+5s≤50
{2t+s≤150

{5t+3s≤150
{t+2s≤50

{5t+3s≤50
{t+2s≤150

{3t+5s≤150 ***
{2t+s≤50

thank you!

{3t+5s≤150

The correct system of inequalities that represents this situation is:

{3t + 5s ≤ 150
{2t + s ≤ 50

Explanation:
To determine the system of inequalities, we need to consider the given information.

We are given that it costs Amanda $3 to make each T-shirt and $5 to make each sweatshirt. So, the total cost of materials for T-shirts can be represented as 3t and the total cost of materials for sweatshirts can be represented as 5s.

We are also given that Amanda has budgeted $150 for materials for the shirts. This means that the total cost of materials for T-shirts and sweatshirts combined should be less than or equal to $150. Hence, the first inequality is 3t + 5s ≤ 150.

Additionally, we are told that Amanda only has 50 hours to sew the shirts. It takes her 2 hours to sew a T-shirt and 1 hour to sew a sweatshirt. So, the total time it takes to sew T-shirts can be represented as 2t and the total time it takes to sew sweatshirts can be represented as s.

Therefore, the total time it takes to sew T-shirts and sweatshirts combined should be less than or equal to 50 hours. Hence, the second inequality is 2t + s ≤ 50.

Combining these two inequalities, we get the correct system of inequalities:

{3t + 5s ≤ 150
{2t + s ≤ 50

I agree with you.