Question

1. multi-step jeds online music club allows him to download 25 songs per month for $14.99. additional songs cost $1.29 each. a. write an inequality to represent this situation. let t be his monthly spending limit and m represent the total number of songs downloaded. a 1.29m ≤ t + 10.01 b 1.29m ≤ t + 17.26 c 1.29t ≤ m + 10.01 d 1.29t ≤ m + 17.26 b. which of the following statements best describes the number of songs jed can download each month without going over his spending limit? a jed will not go over his spending limit of $30 if he downloads 37 songs. b jed will not go over his spending limit of $40 if he downloads 45 songs. c jed can download a maximum of 36 songs if his budget is $30. d jed can download a maximum of 36 songs if his budget is $40. c. suppose that the music club changes its plan so that 50 songs can be downloaded a month. how will the inequality representing this inequality change? a the coefficient of t will decrease. b the coefficient of t will increase. c the coefficient of m will increase. d the constant will increase.

Explanation:

Step1: Solve part a

The cost for \(m\) songs: The first 25 songs cost \(14.99\). If \(m\geq25\), the cost \(C = 14.99+1.29(m - 25)=1.29m+14.99 - 32.25=1.29m - 17.26\). Since \(C\leq t\), we have \(1.29m\leq t + 17.26\).

Step2: Solve part b

For option A: If \(t = 30\), then \(1.29m\leq30 + 17.26=47.26\), \(m=\frac{47.26}{1.29}\approx36.64\). If \(m = 37\), \(1.29\times37-17.26=47.73 - 17.26 = 30.47>30\).
For option B: If \(t = 40\), then \(1.29m\leq40 + 17.26=57.26\), \(m=\frac{57.26}{1.29}\approx44.4\). If \(m = 45\), \(1.29\times45-17.26=58.05 - 17.26=40.79>40\).
For option C: If \(t = 30\), \(m=\frac{30 + 17.26}{1.29}\approx36.64\), maximum \(m = 36\).
For option D: If \(t = 40\), \(m=\frac{40+17.26}{1.29}\approx44.4\).

Step3: Solve part c

Original cost formula: \(C = 14.99+1.29(m - 25)\). New cost formula: \(C'=14.99+1.29(m - 50)=1.29m+14.99 - 64.5=1.29m - 49.51\). The constant term in the inequality \(1.29m\leq t+(\text{constant})\) changes from \(- 17.26\) to \(-49.51\) (more negative). The coefficient of \(m\) (\(1.29\)) and \(t\) (\(1\)) remains the same.

Answer:

a. B. \(1.29m\leq t + 17.26\)
b. C. Jed can download a maximum of 36 songs if his budget is \(\$30\).
c. D. The constant will increase.