Final answer:
To determine how many additional minutes it will take for Sprint and Verizon cell phone plans to cost the same, one must solve the equation 39.99 + 0.45x = 44.99 + 0.40x. The solution reveals that at 100 additional minutes, both plans will have the same cost.
Step-by-step explanation:
The student is asking how many additional minutes it will take for two cell phone plans from Sprint and Verizon to cost the same. To solve this, we can set up an equation where the cost of Sprint's plan plus the additional minutes is equal to the cost of Verizon's plan plus its additional minutes.
Let Sprint's plan be represented by $39.99 + $0.45x (where x is the number of additional minutes). For Verizon's plan, it will be $44.99 + $0.40x.
To find the break-even point, we set the two expressions equal to each other:
39.99 + 0.45x = 44.99 + 0.40x
Now, let's solve for x:
- Subtract 39.99 from both sides: 0.45x = 44.99 - 39.99 + 0.40x
- Combine like terms: 0.45x - 0.40x = 5
- 0.05x = 5
- Divide both sides by 0.05: x = 100
Therefore, it will take 100 additional minutes for both plans to cost the same amount.