Question

You want to buy at least 6 new ringtones from a website, but you cannot spend more than $15. Premium ringtones, x, cost $1.50, and top-10 ringtones, y, cost $3. Which system of inequalities represents this situation?

a) 1.5x + 3y ≤ 15, x + y ≥ 6
b) 1.5x + 3y ≤ 15, x + y ≤ 6
c) 1.5x + 3y ≥ 15, x + y ≤ 6
d) 1.5x + 3y ≥ 15, x + y ≥ 6

Answer 1

The system of inequalities that represents the situation of buying at least 6 ringtones without spending more than $15, with premium ringtones costing $1.50 and top-10 ringtones costing $3, is a) 1.5x + 3y ≤ 15, x + y ≥ 6.

Step-by-step explanation:

The situation described in the student's question involves purchasing at least 6 new ringtones without spending more than $15. Premium ringtones, designated as x, cost $1.50 each, while top-10 ringtones, designated as y, cost $3 each. To represent this scenario, we need to establish two inequalities.

The first inequality will ensure that the total cost does not exceed $15, which can be written as 1.5x + 3y ≤ 15. The second inequality will ensure that the student buys at least 6 ringtones, which translates to x + y ≥ 6.

Combining both inequalities gives us the system that represents the situation: a) 1.5x + 3y ≤ 15, x + y ≥ 6.