Question

For her birthday, Samantha received a gift card, with a value of $200, to a department store. She wants to purchase at least 5 articles of clothing for work. At the store, sweaters cost $24.49 each and dress pants cost $36.99 each. If Samantha does not spend more than the amount on the gift card, which system of inequalities could be used to determine the number of sweaters, s, and the number of dress pants, p, she can buy? A. s + p $200 B. s + p > 5 $24.49s + $36.99p 5 $36.99s + $24.49p < $200

Answer 1

The correct system of inequalities is:

`\left \{ {{s + p \geq 5} \atop {24.99s + 36.99p \leq 200}} \right.`

Explanation:

Since Samantha wants to buy at least 5 pieces of clothing, this means that the total of clothing she buys can be 5 or more, then the sum of sweaters and dress pants she have to buy is:

`s + p \geq 5`

She can't spend more than the gift card, this means that the number of clothing pieces she buys multiplied by its cost must be less or equal to the card's value, so she has to spend:

`24.99*s + 36.99*p \leq 200`

Therefore the correct system of inequalities is:

`\left \{ {{s + p \geq 5} \atop {24.99s + 36.99p \leq 200}} \right.`