Answer Key (Pgs. 5 of Handout Packet)

1. An airplane can hold at most 853 passengers. 532 people have already bought tickets. How many more passengers can buy tickets for the plane? Passengers = p

532 + p < 853

532 + p < 853 - 532 - 532 p < 321 passengers

2. A cab charges a flat fee of $2.00 per ride plus 64 cents per mile. You have $10 in your wallet. How many miles could you ride in the cab and stay below $10?

Miles = m

2 + .64m < 10

2 + .64m < 10 - 2 - 2 .64m < 8 .64 .64

m < 12.5 miles

3. Jorge has $45 to spend on food for his daughter’s birthday party. He spent $27 on hamburgers, buns, candy and drinks. How many packs of $3 hot dogs can he buy and still keep below $45? Packs of hot dogs = p

27 + 3p < 45

27 + 3p < 45 - 27 - 27 3p < 18 3 3 p < 6 (5, 4, 3, 2, or 1 pack(s) of hot dogs)

4. Salisa needs to save a total of $215 to buy concert tickets. She has already saved $15 and earns $20 per week babysitting. How many weeks does she need to work to earn the minimum to buy the concert tickets?

Weeks = w

15 + 20w > 215

15 + 20w > 215 - 15 -15 20w > 200 20 20 w > 10 (10 weeks) 5. Tavares works part time and earns $9 per hour. He needs to earn at least $250 per week to pay his bills. How many hours does he need to work each week to pay his bills?

Hours = h

9h > 250

9h > 250 9 9

h > 27.7 (28 hours)

6. An online music club charges a $12.95 one-time fee for customers to join and 49 cents for each download. Enrique received a $25 music gift card for his birthday. How many songs can he download before the card runs out?

Downloads = d

12.95 + .49d < 25

12.95 + .49d < 25 - 12.95 -12.95 .49d < 12.05 .49 .49

d < 24.59 (24 downloads since he could not download part of a song) Graphing Answers (Pg. 15)

1. y = 2x + 4 2. x + 2y = 6 -x - x 2y = - x + 6 2 2

y = -x + 3 2

3. 2x + 4y = 4 4. y = 1 x - 2 -2x -2x 2 4y = - 2x + 4 4 4

y = -x + 1 2 5. y = 2 x + 1 6. y = -1 x + 2 3 3

7. 2y = 6x + 4 8. 3y = 5x – 3 2 2 3 3

y = 3x + 2 y = 5x – 1 3 Inequalities Practice Answers (Pgs. 19 and 20 in Packet)

1. A gym charges a $48 membership fee per month or $8 per visit. How many visits a month can you make without spending the amount of the membership fee or more?

Visits = v

8v < 48

8v < 48 8 8

v < 6 (What answers make sense? 5, 4, 3, 2, 1, 0)

2. Bekah would like to place a percentage of her monthly income in a savings account each month so that she has at least $2000 at the end of the year. Her monthly income is $2300 after taxes. At least what percentage does she need to set aside?

Percentage of income = p There are 12 months in a year

12(2300)p > 2000

27600p > 2000 27600 27600

p > 7.25%

3. A building contractor has been hired to construct a restaurant patio that is 21 feet in length and has an area no larger than 840 square feet. Considering that for a rectangle, area = length times width, what are the possible values for width? Width = w length times width = area The area must be less than or equal to 840

21w < 840

21w < 840 21 21

w < 40 (What answers make sense? 39 down to 1)

4. A taxicab company charges a base fee of $3.95 plus $1.20 per mile. Megan has $18 to spend on a cab ride. How far could she go?

Distance = d

3.95 + 1.2d < 18

3.95 + 1.2d < 18 -3.95 -3.95 1.2d < 14.05 1.2 1.2

d < 11.7 (What answers make sense? Anything from .1 of a mile to 11.7 miles)

5. Salvador needs to save $3280 to visit relatives in Mexico next year. He earns $2,152 per month working at a packaging plant. Salvador’s expenses are $1,267 a month. Which inequality represents how many months Salvador will need to save to reach his goal? a. 2152m – 1267 ≥ 3280 b. m(2152 – 1267) ≥ 3280 c. 422 2/3 m ≤ 3280 d. 3280 + m ≤ 2152 – 1267

6. A triangle has sides that measure 18 inches, seven inches, and c inches. The perimeter, or total distance around the sides, is greater than 34. What are the possible values for c? Perimeter of a triangle: a + b + c = p

18 + 7 + c > 34

25 + c > 34 - 25 - 25 c > 9

7. A newborn’s mother wants to make sure her son weighs at least 23 pounds by his first birthday. The baby was eight pounds when he was born. How many pounds does he need to gain each month? a. > ¾ pounds Pounds per month = p There are 12 months in a year 8 + 12p ≥ 23 b. ≥ 1 pound c. ≥ 1 ¼ pounds 8 + 12p ≥ 23 d. < 1 2/3 pounds - 8 - 8 12p ≥ 15 12 12

P ≥ = = 1

8. Kataryna has been offered a new job at an accounting firm. She will make $18.15 per hour plus $250 for every new account she attracts. If she works 40 hours a week and signs a new client every week, how many full weeks will it take her to earn at least $10,000? Weeks = w (18.15)(40)x + 250w ≥ 10,000

(18.15)(40)x + 250w ≥ 10,000

740w + 250w ≥ 10,000

990w ≥ 10,000 990 990

w ≥ 10.1 (11 Full Weeks)

9. A political poll about a candidate has a margin of error of ± 2%. The poll result is 46% in favor of the candidate. The candidate wants to increase her popularity to greater than 50% plus 2% to take into account the margin of error. Place one of the numbers or symbols below in each box to compose an inequality to represent the amount that the candidate needs to raise her popularity. You may use a number or symbol more than once, and you may not need every number or symbol. 0.46 + x ≥ 0.5 + 0.02