Question

1. slope - intercept form (word problem) a cell phone plan charges $20 per month plus $0.10 per text. another plan charges $10 per month plus $0.25 per text. let x be the number of texts and y be the total monthly cost. write and solve the system. y = 0.10x + 20 y = 0.25x + 10 space for work

Explanation:

Step1: Set the two equations equal

Since \(y = 0.10x + 20\) and \(y=0.25x + 10\), we set \(0.10x + 20=0.25x + 10\).

Step2: Solve for \(x\)

Subtract \(0.10x\) from both sides: \(20 = 0.15x+10\).
Subtract \(10\) from both sides: \(10 = 0.15x\).
Divide both sides by \(0.15\): \(x=\frac{10}{0.15}=\frac{1000}{15}=\frac{200}{3}\approx66.67\).

Step3: Solve for \(y\)

Substitute \(x = \frac{200}{3}\) into \(y = 0.10x + 20\).
\(y=0.10\times\frac{200}{3}+20=\frac{20}{3}+20=\frac{20 + 60}{3}=\frac{80}{3}\approx26.67\).

Answer:

\(x=\frac{200}{3}\), \(y=\frac{80}{3}\)