Questions: Aisha has 100 saved from her job. She wants to b represents her spending, where x is the number of 4x + 5y < 100 Which ordered pair (x, y) represents a combination (16,8) (15,8) (9,13) (6,15) (5,16)

Solution Steps

To determine which ordered pair \((x, y)\) satisfies the inequality \(4x + 5y < 100\), we will substitute each pair into the inequality and check if the inequality holds true. The pair that satisfies the inequality is the correct answer.

We start with the inequality given in the problem: \[ 4x + 5y < 100 \]

We will substitute each ordered pair \((x, y)\) from the list into the inequality to check which pair satisfies it.

1. For \((16, 8)\): \[ 4(16) + 5(8) = 64 + 40 = 104 \quad (\text{not valid}) \]
2. For \((15, 8)\): \[ 4(15) + 5(8) = 60 + 40 = 100 \quad (\text{not valid}) \]
3. For \((9, 13)\): \[ 4(9) + 5(13) = 36 + 65 = 101 \quad (\text{not valid}) \]
4. For \((6, 15)\): \[ 4(6) + 5(15) = 24 + 75 = 99 \quad (\text{valid}) \]
5. For \((5, 16)\): \[ 4(5) + 5(16) = 20 + 80 = 100 \quad (\text{not valid}) \]

The only ordered pair that satisfies the inequality \(4x + 5y < 100\) is \((6, 15)\).

Final Answer