Questions: Mia had 22. Then she started to receive 4 a week as an allowance. She plans to save all of her money for a bicycle and draws a graph of her planned savings. Mia lets x represent the number of weeks she has received her allowance, and y represent her total amount of money. Which of the following ordered pairs is on Mia's graph? (2,44) (5,42) (1,22) (6,24)

Mia had 22. Then she started to receive 4 a week as an allowance. She plans to save all of her money for a bicycle and draws a graph of her planned savings. Mia lets x represent the number of weeks she has received her allowance, and y represent her total amount of money. Which of the following ordered pairs is on Mia's graph? (2,44) (5,42) (1,22) (6,24)
Transcript text: Mia had $\$ 22$. Then she started to receive $\$ 4$ a week as an allowance. She plans to save all of her money for a bicycle and draws a graph of her planned savings. Mia lets $x$ represent the number of weeks she has received her allowance, and $y$ represent her total amount of money. Which of the following ordered pairs is on Mia's graph? $(2,44)$ $(5,42)$ $(1,22)$ $(6,24)$
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Solution

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Solution Steps

To determine which ordered pair is on Mia's graph, we need to establish the equation that represents her savings over time. Mia starts with $22 and receives an additional $4 each week. This can be represented by the linear equation \( y = 4x + 22 \), where \( x \) is the number of weeks and \( y \) is the total amount of money. We will substitute the \( x \)-values from each ordered pair into the equation to see if the resulting \( y \)-value matches.

Step 1: Establish the Linear Equation

Mia starts with an initial amount of \$22 and receives an additional \$4 each week. This situation can be modeled by the linear equation:

\[ y = 4x + 22 \]

where \( x \) is the number of weeks and \( y \) is the total amount of money.

Step 2: Verify Each Ordered Pair

We need to check which of the given ordered pairs \((x, y)\) satisfies the equation \( y = 4x + 22 \).

  1. For \((2, 44)\): \[ y = 4(2) + 22 = 8 + 22 = 30 \quad (\text{not } 44) \]

  2. For \((5, 42)\): \[ y = 4(5) + 22 = 20 + 22 = 42 \]

  3. For \((1, 22)\): \[ y = 4(1) + 22 = 4 + 22 = 26 \quad (\text{not } 22) \]

  4. For \((6, 24)\): \[ y = 4(6) + 22 = 24 + 22 = 46 \quad (\text{not } 24) \]

Final Answer

The ordered pair that satisfies the equation is \((5, 42)\). Therefore, the answer is \(\boxed{(5, 42)}\).

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