ALGEBRA

1. Miss Wilson has spent $6 on breakfast using her debit card 5 mornings per week for the past 8 weeks. What is the change in Miss Wilson’s account balance from buying breakfast during this time? Write a multiplication expression. Then find and interpret the product.

Let Miss Wilson’s original account balance be X.
Weekly expenditure on breakfast = ($6 x 5days)
= $30
Total expenditure over the 8weeks period = ($30 x 8 weeks)
=$240

Miss Wilson’s account balance after expenditure = $(X – 240)
The change in the account balance = the original account balance – the new account balance
=$[X – (X-240)]
2. Tom drank quarts of water and his sister Jane drank 1.75 quarts of water. Write the amount that Jane drank using a fraction. Who drank more water?

The amount that Jane drunk in fraction = 1 75/100
= 1
Jane drunk more water than Tom

3. The diameter of Earth’s moon is on average m. Use the formula to find the approximate surface area. (Use 3.14 for the value of .)

Radius(r) = (3.8 x 108)/2
= (380,000,000/2) m
=190,000,000 m
Area
= 4(3.14 x 190,000,000 x 190,000,000)
= (4.53416 x 1017) m2

4. Cindy bought a car for $21,330. A few years later, she sold the car for $19,700. Find the percent of change in the value.
Change = $19,700 – $21,330
= -$1630
Percentage change = (change/the buying price) x 100%
= (-1630/21,330) x 100%
= – 7.64%

5. The hard drive in Meredith’s new computer is 1.5 TB, which has a storage capacity of bytes. Her old computer had a hard drive that stored 120 GB, or . How many times larger is the storage capacity of Meredith’s new hard drive?
[(1.5 x1012)/ (1.2 x1011)] = 12.5
The new storage is 12.5 larger than the old one.

6. Karen buys 2 packages of printer paper for $5.79 each, a box of pens for $9.25, a box of paperclips for $2.29, and a calendar for $12.50. If a 6.25% sales tax is added, what is the total cost of Karen’s purchase?
Printer paper (2 x $5.79) = $11.58
Pens = $9.25
Paperclips = $2.29
calendar = $12.50
total sales = $35.62
tax = 6.25/100 x 35.62
= $2.23
Total cost = $35.62 + $2.23
= $37.85
7. A music teacher charged $80.25 for hours. What was the hourly fee to the nearest cent?
$80.25 is charged in 2.5hrs
Hourly charge = [(1 x 80.25)/ 2.5]
= $32.10

8. Abbey is stacking boxes of candles for a store display. The volume of each cube-shaped box is 125 cubic inches. If the display has six layers of boxes, how high is the display?
V = S * S * S
125in3 = S * S * S
S = 5inches
high is the display = 5inches x 6
= 30 inches

9. A student measured the temperature in degrees Celsius for several winter days and recorded the data in a list. Find the average of the temperatures listed.

[6 + (-7) + (-5) + 5 + (-8) + 3]/6 = -1

10. Elsie pays $8.99 for a one-pound canister of Georgia pecans. Write and solve a proportion to determine the cost of 4 ounces of the pecans she needs for a particular recipe. (Round answer to the nearest cent.)
1 pound = 16 ounces
4 ounces will be equivalent to [(4 x 1)/16] = 0.25 pounds
1 pound of pecan = $8.99
0.25 pounds = 0.25 x $8.99
= $2.25

11. How many kilometers is it from the main gate to Manatee Springs? (Hint: To convert from yards to kilometers, multiply by 0.0009144). Round answer to the nearest hundredth kilometer.

Distance between main gate to Manatee Springs = 1500 yards +2000yards
= (3500yards x 0.0009144)
= 3.2 kilometers

12. Out of the 21 students in Mrs. Clark’s class, of the class are boys and of the class are girls. How many students in the class are girls and how many are boys?
Boys (3/7 x 21) = 9
Girls (4/7 x 21) = 12

13. Jacob is saving to buy an MP3 player that costs $195. He earns $225 a week at a part-time job. His expenses are $180 a week. If he currently has saved $55, how many more weeks will it be before he can buy the MP3 player?
Weekly savings = $225 – $180
= $45
Amount remaining = $195 – $55
= $140
140/45 = 3.11 weeks
It will take Jacob approximately 3 more weeks before he can purchase the MP3 player.

14. Blank CDs come in spindles of 25 or 60. Rachel needs 230 blank CDs for her eighth grade science class. How many spindles of each amount should she buy?
The GCD of 25,60 and 230 is 5. Therefore, Rachel will require 5 spindles in total.
Options: 60 x 3 = 180 60 x 2 = 120
25 x 2 = 50 25 x 3 = 75
Rachel should buy 3, 60 spindles and 2, 25spindles

15. Charles deposited $12,000 in the bank. He withdrew $5000 from his account after one year. If he receives a total amount of $9340 after 3 years, find the rate of simple interest.
Principal after the first year =$12,000 – $5000
= $7,000
Interest = $9340 – $7,000
= $2340
Simple interest = principal x interest rate x time
$2340 = 7000 * x *3
2340 = 21000x/100
234000 = 21000x
X = 11.14%

16. Bev earns $2 a week for taking out her neighbor’s trash cans. Complete the table of values. Then state the domain and range.

Use the information in the table below to answer the following questions.

17. How much more will the total cost of three adult tickets be than three children tickets?
($22 x 3) – ($15 x 3)
$66 – $45 = $21
18. The mass of a small virus is kg. The mass of an average human cell is kg. Which of the two has a lesser mass? How many times less is it?
The virus has a lesser mass compared to the mass of a human cell
[(10-12) kg/ (10-20) kg] = 100,000,000
The mass of the virus is 100 million times less.

19. In a concert hall, 250 seats out of 300 seats were occupied. To the nearest thousandth, what part of the hall was not occupied?
300 – 250 = 50 unoccupied seats
Unoccupied part = 50/300
= 0.167
20. The difference between Maggie’s age and Terrance’s age is 3. If x represents Maggie’s age and y represents Terrance’s age, make a table of possible values for x and y. Graph the ordered pairs and describe the graph.
Maggie – x
Terence – y
y-X = 3