Question

You would like to purchase a new pair of running shoes X and a pair of running shorts Y. You have $150 to spend. Which of the following inequalities represents this situation?

a) X + Y < 150

b) X + Y > 150

c) X + Y = 150

d) X - Y > 150

Answer 1

The inequality that represents the situation of spending no more than $150 on running shoes X and shorts Y is X + Y ≤ 150. The closest option provided is (a) X + Y < 150.

Step-by-step explanation:

The question is asking which inequality represents the situation where a student has $150 to spend on a new pair of running shoes X and a pair of running shorts Y. To represent this mathematically using an inequality, we need an expression that will show the sum of the cost of the shoes and shorts against the student's budget. The correct inequality should indicate that the total cost should be less than or equal to the available budget of $150. Therefore, the suitable inequality is X + Y ≤ 150. However, between the provided options, the closest one is option (a), X + Y < 150, which indicates that the sum of the prices of the shoes and shorts must be less than the budget, implying that the student cannot spend more than $150.