Question

Brandi is downloading music for her MP3 player. Albums cost $10 each, and singles cost $1 each. She wants to purchase at least 5 singles but wants to spend no more than $25 total. If Brandi purchases x albums and y singles, which of the following is a possible combination of albums and singles that Brandi could purchase and stay within her guidelines?

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5 albums and 2 singles
2 albums and 5 singles
2 albums and 10 singles
10 albums and 2 singles

Answer 1

Let x = albums, y = singles. Constraints: y ≥ 5 and 10x + y ≤ 25.

Check each choice:
- 5 albums and 2 singles: y = 2 < 5 and 10·5+2 = 52 > 25 → invalid.
- 2 albums and 5 singles: y = 5 and 10·2+5 = 25 ≤ 25 → valid.
- 2 albums and 10 singles: 10·2+10 = 30 > 25 → invalid.
- 10 albums and 2 singles: y = 2 < 5 and 10·10+2 = 102 > 25 → invalid.

Thus the possible combination is 2 albums and 5 singles.