EOC BootCamp Question Set 1

1. 1. A delivery service charges $6.25 for the first pound and $1.75 for each additional pound. Another company charges a flat rate of $4 per pound. The equation 6.25 + 1.75(p - 1) = 4p determines the weight (p) at which both companies charge the same amount. Solve for p.

• 2 pounds

• 3 pounds

• 4 pounds

• 5 pounds

2. 2. Two rectangular garden plots have the same area in square yards. What value of x (in yards) makes this statement true?

• 7(3x) = 9x

• 7(x + 3) = 9x

• 7 + (x + 3) = x + 9

• 2(x + 3) = 2(x + 9)

3. 3. During an international competition, Team A won 7 more than twice the number of medals won by Team B. Together, the two teams won a total of 40 medals. Identify the equation that represents this scenario, where b represents the number of medals won by Team B.

• 7 + 2b + b = 40

• 2b + b = 40

• 2(b + 7) = 40

• 2b + 7 - b = 40

6. 6. A mathematical statement is given below that can be modeled with an inequality. Write an inequality in the space provided, using the variable "x" to represent the missing number. Do not solve or simplify. Statement: The sum of 8 times a number and 5 is greater than or equal to 50.

• 8x + 5 ≥ 50

• 8x + 5 < 50

• 8x - 5 ≥ 50

• 8x + 5 = 50

• Limited Solutions

• No Solution

• Infinite Solutions

• Cannot be determined

8. 8. Identify the inequality that models this real-world situation, where g represents the number of gigabits. A new phone carrier, TalkPlus, charges $185 per month for unlimited calls and text, plus $12 per gigabit of data. Another carrier, FastConnect, charges $39.50 per gigabit with unlimited talk and text included. Which inequality correctly represents the case where TalkPlus is more expensive than FastConnect?

• 185 - 12g > 39.50g

• 185 + 12g > 39.50g

• 185 + 120g < 39.50g

• 185 + 12g > 39.50

9. 9. Solve the compound inequality: -6n + 18 ≥ 60 or 3n - 9 > 24

• n > 11 or n ≥ -7

• n < 11 or n ≤ -7

• n > 11 or n ≤ -7

• -7 ≤ n < 11

• 
• 
• 
• 

• x = 1, -11

• x = 1, -5

• x = 6, -16

• x = 6, -5

13. 13. A bottling machine is programmed to fill each bottle with 20 fluid ounces of juice. After filling, another machine checks the weight. If the actual amount is 0.4 fluid ounces more or less than the target, the bottle is rejected. Which equation represents the minimum and maximum amounts of juice that will be accepted?

• |x + 20| = 0.4

• |x - 20| = 0.4

• |x - 0.4| = 20

• |x + 0.4| = 20