60. multi-step jeds online music club allows him to download 25 songs per month for $14.99. additional songs…

60. 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.

60. 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.

Answer

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.