Question
10. Jacob and Sam both pay for a streaming service. Jacob pays a \( \$ 50 \) upfront fee plus \( \$ 15 \) per month. Sam pays \( \$ 25 \) per month. After how many months will Jacob and Sam have paid the same total amount?
Ask by Kelley Lee. in the United States
Jan 25,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
After 5 months, Jacob and Sam will have paid the same total amount.
Solution
To determine after how many months Jacob and Sam will have paid the same total amount for the streaming service, let's set up an equation based on their payment structures.
**Jacob's Total Cost:**
Jacob pays an upfront fee of \$50 plus \$15 per month.
\[ \text{Jacob's Cost} = 50 + 15m \]
where \( m \) is the number of months.
**Sam's Total Cost:**
Sam pays \$25 per month.
\[ \text{Sam's Cost} = 25m \]
**Setting the Costs Equal:**
To find the number of months where both have paid the same amount:
\[ 50 + 15m = 25m \]
**Solving for \( m \):**
1. Subtract \( 15m \) from both sides:
\[ 50 = 10m \]
2. Divide both sides by 10:
\[ m = 5 \]
**Verification:**
- **Jacob:** \( 50 + 15 \times 5 = 50 + 75 = \$125 \)
- **Sam:** \( 25 \times 5 = \$125 \)
After **5 months**, both Jacob and Sam will have paid the same total amount of \$125.
**Answer:**
5
Reviewed and approved by the UpStudy tutoring team
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Explain 
Simplify this solution Beyond the Answer
Let's break it down! Jacob's total payment over \( x \) months is given by the formula: \( 50 + 15x \). Sam’s total payment over the same period is \( 25x \). We want to find \( x \) such that: \[ 50 + 15x = 25x \] Solving this equation, we first subtract \( 15x \) from both sides: \[ 50 = 25x - 15x \] This simplifies to: \[ 50 = 10x \] Now, divide both sides by 10: \[ x = 5 \] So, after 5 months, both Jacob and Sam will have paid the same total amount! How cool is that?
