Question

10 systems of equations: word problem practice objective: use the desmos graphing calculator to solve these real - world scenarios. for the first five, the equations are provided. for the last five, you must write the equations before graphing. the smartphone plans phone plan a costs $30 per month plus $0.05 per text message. phone plan b costs $10 per month plus $0.15 per text message. how many texts (x) would make the monthly bill (y) the same for both plans?

Explanation:

Step1: Define equations for each plan

For Plan A, the cost \( y \) is the monthly fee plus the cost per text times the number of texts \( x \). So, \( y = 30 + 0.05x \).
For Plan B, the cost \( y \) is \( y = 10 + 0.15x \).

Step2: Set the equations equal to each other

To find when the costs are the same, set \( 30 + 0.05x = 10 + 0.15x \).

Step3: Solve for \( x \)

Subtract \( 0.05x \) from both sides: \( 30 = 10 + 0.10x \).
Subtract 10 from both sides: \( 20 = 0.10x \).
Divide both sides by 0.10: \( x = \frac{20}{0.10} = 200 \).

Answer:

200