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)

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

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Solution Steps

To determine which ordered pair (x,y)(x, y) satisfies the inequality 4x+5y<1004x + 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.

Step 1: Define the Inequality

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

Step 2: Substitute Ordered Pairs

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

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

The only ordered pair that satisfies the inequality 4x+5y<1004x + 5y < 100 is (6,15)(6, 15).

Final Answer

The answer is (6,15)\boxed{(6, 15)}.

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