d. applications using equations: (use a separate sheet of paper to complete the following)\n8. your long…

d. applications using equations: (use a separate sheet of paper to complete the following)\n8. your long distance telephone provider offers two plans. plan a has a monthly fee of $15 and $0.25 per minute. plan b has a monthly fee of $20 and $0.05 per minute. write and solve an equation to find the number of minutes that you must talk to have the same cost for each of the plans.\n9. for the past three months, grace used her cell phone for 43 minutes, 62 minutes, and 57 minutes. how many minutes would she have to use her cell phone this month for the average usage over the four months to be 55 minutes?\n10. a triangle has one angle measuring 3x degrees. a second angle measures (2x + 20) degrees and the third angle measures (4x - 20) degrees. what is the value of x?\n11. a rope 25 feet long is cut into 3 pieces. the first piece is 2x feet long, the second piece is 5x feet long, and the third piece is 4 feet long.\n a. write and solve an equation to find x.\n b. find the lengths of the first and second pieces.\n12. the average of your 3 quiz grades is 17 points. two of your quiz grades are 14 points and 19 points. write and solve an equation to find the score of your third quiz.\n13. the cost c (in dollars) of making n feet of cabinet is represented by c = 18n + 45. how many feet of cabinet are made when the cost is $441?\n14. at the movies, you order 3 boxes of popcorn and a bottle of water. the cost of a bottle of water is $1.75. your total cost is $9.25. write and solve an equation to find the cost of one box of popcorn.\n15. you and your friend each purchase an equal number n of magazines. your magazines cost $1.50 each and your friends magazines cost $2 each. the total cost for you and your friend is $10.50. write and solve an equation to find the number of magazines you purchased.

d. applications using equations: (use a separate sheet of paper to complete the following)\n8. your long distance telephone provider offers two plans. plan a has a monthly fee of $15 and $0.25 per minute. plan b has a monthly fee of $20 and $0.05 per minute. write and solve an equation to find the number of minutes that you must talk to have the same cost for each of the plans.\n9. for the past three months, grace used her cell phone for 43 minutes, 62 minutes, and 57 minutes. how many minutes would she have to use her cell phone this month for the average usage over the four months to be 55 minutes?\n10. a triangle has one angle measuring 3x degrees. a second angle measures (2x + 20) degrees and the third angle measures (4x - 20) degrees. what is the value of x?\n11. a rope 25 feet long is cut into 3 pieces. the first piece is 2x feet long, the second piece is 5x feet long, and the third piece is 4 feet long.\n a. write and solve an equation to find x.\n b. find the lengths of the first and second pieces.\n12. the average of your 3 quiz grades is 17 points. two of your quiz grades are 14 points and 19 points. write and solve an equation to find the score of your third quiz.\n13. the cost c (in dollars) of making n feet of cabinet is represented by c = 18n + 45. how many feet of cabinet are made when the cost is $441?\n14. at the movies, you order 3 boxes of popcorn and a bottle of water. the cost of a bottle of water is $1.75. your total cost is $9.25. write and solve an equation to find the cost of one box of popcorn.\n15. you and your friend each purchase an equal number n of magazines. your magazines cost $1.50 each and your friends magazines cost $2 each. the total cost for you and your friend is $10.50. write and solve an equation to find the number of magazines you purchased.

Answer

Explanation:

Step1: Set up the cost equations for Plan A and Plan B

Let (x) be the number of minutes. The cost of Plan A, (C_A = 15+0.25x) The cost of Plan B, (C_B=20 + 0.05x)

Step2: Set (C_A = C_B) and solve for (x)

[ \begin{align*} 15+0.25x&=20+0.05x\ 0.25x-0.05x&=20 - 15\ 0.2x&=5\ x&=\frac{5}{0.2}\ x& = 25 \end{align*} ]

Answer:

The number of minutes is (25)