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**Technology Trends**

In the United States, about three-fourths of 12- to 17-year-olds use a cell phone daily. Nearly all teens use their cell phones to take pictures, about 55% play games, about 35% download games, and about 50% use the calendar to organize and schedule social events.

Today you will investigate cell phones and their features. You will write one- and two-step equations to solve problems. You will review and apply the algebra terms and concepts you learned in this unit.

As you complete this task, keep these questions in mind:
- How can equations be used to represent real-world problems?
- What are the steps I need to follow to solve for an unknown variable?

**Directions:**

Complete each of the following tasks, reading the directions carefully as you go.

You will be graded on the work you show, or your solution process, in addition to your answers. Make sure to show all of your work and to answer each question as you complete the task. Type all of your work into this document so you can submit it to your teacher for a grade. You will be given credit based on the work you show and the completeness and accuracy of your explanations.

Your teacher will give you further directions on submitting your work. You may be asked to upload the document, email it to your teacher, or hand in a hard copy.

Now let’s get started!

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**Step 1: Using One-Step Equations to Solve Problems**

a) Suppose you send about 12 text messages a day, and your older sister sends more text messages than you do. Together, you send a total of about 26 messages per day. About how many text messages does she send a day? Write an equation and solve for the unknown value. (2 points)

b) Your father uses text messaging to communicate with his employees. If he sends an average of 19 text messages each day, how many more text messages does he send than you? Write an equation and solve for the unknown value. (2 points)

c) Your parents allow you to have Internet access on your cell phone as long as you prepay the bill. If your bill is $17.50 per week, how much would you have to save per day to pay the bill? Describe the step-by-step process you use to solve the problem. (3 points)

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**Step 2: Using Two-Step Equations to Solve Problems**

a) You need to download 3 games for your math class. Each game is the same price. Since this is your first time downloading a game from the site, you are also charged a one-time $0.50 access fee. You are charged a total of $4.35. What is the cost of each game? Show your work and round your answer to the nearest cent. (2 points)

b) Your mother has a new cell phone. It comes with 18 applications already installed. She uses only [tex]\frac{2}{3}[/tex] of those applications. She downloaded an additional 12 applications that she uses regularly. Write an equation to represent the total number of applications your mom uses. Explain your equation and your reasoning. (4 points)

c) How many applications will your mother actually use on her new cell phone? Solve the equation you wrote in part b to find the unknown variable. (2 points)

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**Step 3: Using Multi-Step Equations to Solve Problems**

a) You are using the equation [tex]4(p – 7) = 44[/tex] to determine how many pictures can be saved at one time to the photo stream on your cell phone. Describe the operations in the order that you will perform them to solve the equation. (3 points)

b) How many pictures can you save at one time to the photo stream on your cell phone? Solve the equation you wrote in part a to find the unknown variable. (2 points)

c) The phone case you want to buy is marked down 30%, and you have a 25% off coupon. You pay $42.00. Can this equation be used to find the original price of the phone case? If so, what is the original price of the item? Explain. (5 points)

Answer :

Final answer:

This answer provides step-by-step explanations for solving one-step equations involving text messages, calculating bill amounts, finding the cost per game, determining the total number of applications, and solving multi-step equations related to saving pictures and pricing. The answer also addresses whether an equation can be used to find the original price of an item.

Explanation:

a) To find the number of text messages your older sister sends per day, you can set up the equation 12 + x = 26, where x represents the number of text messages she sends. To solve for x, subtract 12 from both sides of the equation: x = 26 - 12 = 14. Therefore, your older sister sends about 14 text messages per day.

b) To find the number of text messages your father sends more than you, you can set up the equation x - 12 = 19, where x represents the number of text messages your father sends. To solve for x, add 12 to both sides of the equation: x = 19 + 12 = 31. Therefore, your father sends about 31 more text messages per day than you.

c) To find the amount you need to save per day to pay the cell phone bill, you can set up the equation 7d = 17.50, where d represents the number of days. To solve for d, divide both sides of the equation by 7: d = 17.50 / 7 = 2.50. Therefore, you need to save $2.50 per day to pay the bill.

d) To find the cost of each game, you can set up the equation 3x + 0.50 = 4.35, where x represents the cost of each game. To solve for x, subtract 0.50 from both sides of the equation and then divide by 3: x = (4.35 - 0.50) / 3 = 1.28. Therefore, each game costs about $1.28.

e) To represent the total number of applications your mom uses, you can set up the equation 18 + 12 = (2/3)t, where t represents the total number of applications installed on her new cell phone. To solve for t, subtract 18 from both sides of the equation and then multiply by 3/2: t = (30 - 18) * (3/2) = 12.

f) To determine how many pictures can be saved at one time to the photo stream on your cell phone, you can use the equation 4(p - 7) = 44, where p represents the number of pictures. To solve for p, first distribute the 4 to p and -7: 4p - 28 = 44. Then, add 28 to both sides of the equation and divide by 4: 4p = 72, p = 72 / 4 = 18. Therefore, you can save 18 pictures at one time to the photo stream on your cell phone.

g) No, the equation 0.7x - (0.3)(0.25)x = 42 cannot be used to find the original price of the phone case. This equation is incomplete and does not provide enough information to solve for x. Therefore, the original price of the phone case cannot be determined.

Learn more about One-step and two-step equations

https://brainly.com/question/9585437

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