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?

Question

UpStudy AI · Accepted Answer

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
After 5 months, Jacob and Sam will have paid the same total amount.

Jacob and Sam both pay for a streaming service.
Jacob pays a upfront fee plus per month. Sam
pays per month. After how many months will Jacob
and Sam have paid the same total amount?

Upstudy AI Solution

Answer

Solution

Beyond the Answer

Related Questions

Latest Algebra Questions

Jacob and Sam both pay for a streaming service. Jacob pays a upfront fee plus per month. Sam pays per month. After how many months will Jacob and Sam have paid the same total amount?