To solve this problem, let's denote the cost of each anytime minute as \( m \) (in dollars) and the cost of each text message as \( t \) (in dollars).
From the information provided, we can set up the following equations based on Noah's usage and total payments:
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First month: \[ 200m + 400t = 80 \]
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Second month: \[ 150m + 350t = 67.50 \]
Now, let's simplify these equations.
First month equation:
\[ 200m + 400t = 80 \quad \Rightarrow \quad 2m + 4t = 0.8 \quad \Rightarrow \quad m + 2t = 0.4 \quad \text{(Equation 1)} \]
Second month equation:
\[ 150m + 350t = 67.50 \quad \Rightarrow \quad 15m + 35t = 6.75 \quad \Rightarrow \quad 3m + 7t = 1.35 \quad \text{(Equation 2)} \]
Now we can solve these two equations (Equation 1 and Equation 2):
From Equation 1: \[ m = 0.4 - 2t \]
Substituting \( m \) into Equation 2: \[ 3(0.4 - 2t) + 7t = 1.35 \] \[ 1.2 - 6t + 7t = 1.35 \] \[ 1.2 + t = 1.35 \] \[ t = 1.35 - 1.2 = 0.15 \]
Now substitute \( t = 0.15 \) back into Equation 1 to find \( m \): \[ m + 2(0.15) = 0.4 \] \[ m + 0.3 = 0.4 \] \[ m = 0.1 \]
So we have:
- The cost of each anytime minute \( m = 0.10 \) dollars (or 10 cents).
- The cost of each text message \( t = 0.15 \) dollars (or 15 cents).
Now let's evaluate the given options:
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Each text message costs 5 cents more than each anytime minute.
- True: \( 0.15 - 0.10 = 0.05 \) (5 cents)
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Each anytime minute costs 10 cents more than each text message.
- False: \( 0.10 \) is not more than \( 0.15 \).
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A text message and an anytime minute each cost 25 cents.
- False: They cost 10 cents and 15 cents respectively.
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Each text message costs double the amount of an anytime minute.
- False: \( 0.15 \) is not double \( 0.10 \).
The only true statement is: Each text message costs 5 cents more than each anytime minute.
2 answers