Answer to Question #164344 in Algebra for umni

Question

For each of the problems below define a variable, set up an equation/inequality, solve the inequality, and answer the question  using units. 

1. A membership to X-Sport fitness costs $18 per month plus a one-time fee of 50 dollars to join. If you want to spend no more  than 380 dollars, then how long can you be a member for? 

Define a variable: 

Set up an inequality: 

Solve the inequality: 

2. After 3 days of their fundraiser, the freshman class raised $548. Their goal was to raise $750 or more. What is the least amount  of money they still need to raise in ordered to reach their goal? 

3. Your cell phone plan costs $39.99 per month plus $0.15 for each text message you send or receive. You have at most $55 to  spend on your cell phone bill. What is the maximum number of text messages that you can send or receive next month? 

4. Pam wants to buy a pair of shoes and a hat. She has to spend less than $50.00 for both. If the hat costs $21.95, how much can  she pay for the shoes?

5. You and your friends have a total of $12.00 to spend on a pizza. A large pizza with cheese costs $8.00 plus $0.40 for each  additional topping. Use an inequality to find the number of toppings you can afford. 

6. An amusement park charges $5.00 for admission and $0.80 for each ride. Suppose you go to the park with $15.00. Write an  inequality that represents the possible number of rides you can go on. How many rides can you go on? 

7. You have $32.14 to spend on a shirt. The tax is 6%. How much can the shirt cost so you still have enough money to pay the sales  tax? 

8. Mary is participating in the Secret Santa exchange at her office. The rule is that you cannot spend more than $25 for the entire  week. Mary has already purchased four of the five gifts that she needs to get. Here are the prices of the four gifts: $4.75, $3.15,  $7.39, and $4.50. How much money can Mary spend on the last gift? 

9. You need to raise $130.00 for your uniform for the hockey team. You already have $52.00. You are selling hats for $7.00 each.  How many hats will you have to sell in order to reach your goal? 

10. The hard drive on your computer has a capacity of 120 GB. You have used 85 GB. You want to save some home videos to your  hard drive. What is the maximum size of the video collection you can save?

Answer 1

(1). $50 - one-time fee and $18 - per month

$$50+18x\leq 380 / - 50$$ $$18x \leq 330 / : 18$$ $$x \leq 18.(3)$$

You can be a member for 18 months.

(2). the freshman class raised $548 and er 3 days of their fundraiser, the freshman class raised $750.

the least amount of money they still need to raise in ordered to reach their goal is $750 - $548 = $202

(3). $39.99 - per month and $0.15 - for each text message.

$$39.99+0.15x \leq 50 / - 39.99$$ $$0.15x \leq 10.01 / : 0.15$$ $$x \leq 66.7(3)$$

You send or recieve 66 messages for the month

(4). the hat costs $21.95 and he has to spend less than $50.00 on both

$50.00 - $21.95 = $28.05 She can pay $28.05 for shoes

(5). A large pizza with cheese costs $8.00 plus $0.40 for each additional topping

$8 + 0.4x\leq12 / - 8$

$0.4x \leq4 / : 0.4$

$x \leq 10$

the number of toppings you can afford is 10.

(6) An amusement park charges $5.00 for admission and $0.80 for each ride.

$$5+0.8x \leq 15 / -5$$

$0.8x \leq10/ : 0.8$

$x \leq 12.5$

rides can you go on is 12

(7). $32.14 to spend on a shirt. The tax is 6%.

$1.06x \leq 32.14 \to 30.32$

$30.32 is a cost shirt you still have enough money with taxes.

(8) Here are the prices of the four gifts: $4.75, $3.15, $7.39, and $4.50 and The rule is that you cannot spend more than $25 for the entire week

money can Mary spend on the last gift is $25 - ( $4.75 + $3.15 + $7.39 + $4.50) = $5.21

(9) Ineed to raise $130.00 for your uniform for the hockey team. I have $52.00. I am selling hats for $7.00 each. 

$130.00 = 52+7x \to 11.14$

 I have to sell 12 hats in order to reach my goal

(10) The hard drive on your computer has a capacity of 120 GB. I have used 85 GB.

the maximum size of the video collection I can save is 120 - 85 = 35GB