Question

claim, evidence, reasoning
verizon charges a flat fee of $50 and $0.05 per text. at&t charges a flat fee of $30 and $0.10 per text.
part a: write and solve an equation to find after how many texts will verizon and at&t cost the same amount of money.
verizon
at&t let x = number of texts
part b: how much will it cost for each cell phone company after that many texts?
claim: verizon and at&t will both charge $________ for ________ texts.

Explanation:

Step1: Set up equations

Let \(x\) be the number of texts.
For Verizon, the cost \(C_{V}=50 + 0.05x\).
For AT&T, the cost \(C_{A}=30+0.10x\).
Set \(C_{V}=C_{A}\), so \(50 + 0.05x=30 + 0.10x\).

Step2: Solve the equation

Subtract \(0.05x\) from both sides: \(50=30 + 0.10x-0.05x\).
Simplify: \(50=30 + 0.05x\).
Subtract 30 from both sides: \(50 - 30=0.05x\).
So \(20 = 0.05x\).
Divide both sides by \(0.05\): \(x=\frac{20}{0.05}=400\).

Step3: Find the cost

Substitute \(x = 400\) into Verizon's cost formula: \(C_{V}=50+0.05\times400\).
\(C_{V}=50 + 20=70\).
Substitute \(x = 400\) into AT&T's cost formula: \(C_{A}=30+0.10\times400\).
\(C_{A}=30 + 40=70\).

Answer:

Verizon and AT&T will both charge \(\$70\) for \(400\) texts.