Question

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?
a) {3t+5s≤50
{2t+s≤150
b) {5t+3s≤150
{t+2s≤50
c) {3t+5s≤150
{2t+s≤50
d) {5t+3s≤50
{t+2s≤150

Answer 1

The correct system of inequalities that represents Amanda's situation is option b) {5t+3s≤150{t+2s≤50. Given the costs of making T-shirts and sweatshirts, the inequalities 5t + 3s ≤ 150 and t + 2s ≤ 50 ensure that Amanda stays within her budget and time constraints.

Step-by-step explanation:

The correct system of inequalities that represents Amanda's situation is option b) {5t+3s≤150{t+2s≤50.

Let t represent the number of T-shirts and s represent the number of sweatshirts that Amanda can sew.

Given that it costs $3 to make each T-shirt and $5 to make each sweatshirt, we can set up the inequalities:

For the budget constraint: 5t + 3s ≤ 150

For the time constraint: t + 2s ≤ 50

These inequalities ensure that Amanda stays within her budget of $150 for materials and 50 hours of sewing time.