1.
Jeannine has a bag with 3 videocassettes, 4 marbles, 7 books, and one orange. What is the ratio of books to videocassettes?_{ }
_{â€¢}
Correct Answer
B. 7:3
Explanation
The ratio of books to videocassettes is 7:3 because there are 7 books and 3 videocassettes in Jeannine's bag.
2.
â€¢_{ }
_{â€¢}
_{â€¢}_{Bobby has a bag full of marbles that he keeps in his room. He has 35 red marbles and 25 green marbles. Find the ratio of red marbles to green marbles, and put it in its simplest form. }
Correct Answer
A. 7 to 5
Explanation
The ratio of red marbles to green marbles is 7 to 5. This can be determined by dividing the number of red marbles (35) by the number of green marbles (25). Simplifying this ratio gives us 7/5, which is equivalent to 7 to 5.
3.
Write this ratio one different way:
6/15
Correct Answer
6 to 15
6:15
6to15
Explanation
The given ratio, 6/15, can be written as 6 to 15 or 6:15 or 6to15. These different notations represent the same ratio, where there are 6 parts of one quantity for every 15 parts of another quantity.
4.
Solve for h: 2h + 1 = 9
Correct Answer
C. H = 4
Explanation
The equation given is 2h + 1 = 9. To solve for h, we need to isolate the variable h. Subtracting 1 from both sides of the equation, we get 2h = 8. Dividing both sides by 2, we find that h = 4. Therefore, the correct answer is h = 4.
5.
Which answer is a 'clue word' for division?
Correct Answer
B. Split equally
Explanation
The clue word for division is "split equally" because it suggests that something is being divided into equal parts. This indicates that division is being performed, as division involves dividing a quantity into equal groups or parts. The other options, "product" and "difference," do not relate to division and are not clue words for this operation.
6.
â€¢Jeannie takes inventory of her closet and discovers that she has 8 shirts for every 5 pair of jeans. If she has 40 shirts, how many pairs of jeans does she have?
Correct Answer
C. 25 pairs of jeans
Explanation
Jeannie has 8 shirts for every 5 pairs of jeans. If she has 40 shirts, we can set up a proportion to find the number of pairs of jeans she has. Let x represent the number of pairs of jeans. The proportion can be written as 8/5 = 40/x. Cross multiplying, we get 8x = 200. Dividing both sides by 8, we find that x = 25. Therefore, Jeannie has 25 pairs of jeans.
7.
Solve for x:4x - 1 > 15
Correct Answer
A. X > 4
Explanation
The given inequality is 4x - 1 > 15. To solve for x, we can add 1 to both sides of the inequality to isolate the term with x. This gives us 4x > 16. To solve for x, we can divide both sides of the inequality by 4, resulting in x > 4. Therefore, the correct answer is x > 4.
8.
Write an algebraic expression for "two times a number minus five". Use x as a variable.
Correct Answer
2x - 5
2x- 5
2x -5
2x-5
Explanation
The correct answer is 2x - 5. This expression represents "two times a number minus five" using the variable x. The coefficient 2 indicates that the number is multiplied by 2, and then 5 is subtracted from the result.
9.
Solve for x:-2x + 6 â‰¤ 20
Correct Answer
B. X â‰¥ -7
Explanation
The given inequality is -2x + 6 â‰¤ 20. To solve for x, we first subtract 6 from both sides of the inequality to isolate the term with x. This gives us -2x â‰¤ 14. Then, we divide both sides by -2, remembering to reverse the inequality sign since we are dividing by a negative number. This gives us x â‰¥ -7. Therefore, the correct answer is x â‰¥ -7.
10.
â€¢Solve this proportion:
78 : 162 = x : 193
Correct Answer
A. 92.9
Explanation
The given proportion can be solved by cross-multiplying. Cross-multiplying gives us 78 * 193 = 162 * x. Simplifying this equation gives us 15054 = 162x. To solve for x, we divide both sides of the equation by 162, which gives us x = 92.9. Therefore, the value of x in the proportion is 92.9.
11.
â€¢David read 40 pages of a book in 50 minutes. How many pages should he be able to read in 80 minutes?
Correct Answer
B. 64 pages
Explanation
If David can read 40 pages in 50 minutes, we can set up a proportion to find out how many pages he can read in 80 minutes. We can write the proportion as 40/50 = x/80, where x represents the number of pages he can read in 80 minutes. To solve for x, we cross multiply and get 50x = 3200. Dividing both sides by 50, we find that x = 64. Therefore, David should be able to read 64 pages in 80 minutes.
12.
Shawna reduced the size of a rectangle to a height of 2 in. What is the new width if it was originally 24 in wide and 12 in tall?
Correct Answer
C. 4 inches
Explanation
When Shawna reduces the size of the rectangle, she is keeping the original proportions of the rectangle intact. The original rectangle had a width of 24 inches and a height of 12 inches, resulting in a width-to-height ratio of 2:1. Since Shawna reduces the height to 2 inches, the new width will also be reduced by the same ratio. Therefore, the new width will be 4 inches, maintaining the 2:1 ratio.
13.
State whether these ratios are equal:
69
,
48
Correct Answer
B. These two ratios are not proportions
Explanation
Two ratios are considered proportions if they are equal to each other. In this case, the given ratios of 69 and 48 are not equal to each other, therefore they are not proportions.
14.
Determine whether the change is an increase or decrease. Then obtain the percent of increase or decrease. Round the answer to the nearest whole percent.
old: 345 acres
new: 380 acres
Correct Answer
A. 10.14% increase
Explanation
The percent increase is calculated by finding the difference between the new and old values, dividing that by the old value, and then multiplying by 100. In this case, the difference between the new and old values is 380 - 345 = 35. Dividing that by the old value (345) gives 35/345 â‰ˆ 0.1014. Multiplying by 100 gives 0.1014 * 100 â‰ˆ 10.14. Therefore, the correct answer is 10.14% increase.
15.
The number of participants in an athletic competition increased from 312 to 351. Find the percent of increase.
Correct Answer
B. 12.5% increase
Explanation
The percent of increase can be calculated by finding the difference between the final number of participants and the initial number of participants, dividing that by the initial number of participants, and then multiplying by 100. In this case, the difference is 351 - 312 = 39. Dividing 39 by 312 and multiplying by 100 gives us 12.5%. Therefore, the correct answer is 12.5% increase.
16.
In 1990, Mary's height was 61 cm. In 2000, she grew to 130 cm. Find the percent increase in Mary's height.
Correct Answer
C. 113% increase
Explanation
In 1990, Mary's height was 61 cm and in 2000, her height grew to 130 cm. To find the percent increase in Mary's height, we can use the formula: (new value - old value) / old value * 100. Plugging in the values, we get (130 - 61) / 61 * 100 = 113.11%. Therefore, the percent increase in Mary's height is 113%.
17.
Calculate the percent of change.
Before: $130 After: $270.
Correct Answer
A. 107% increase
Explanation
The percent of change can be calculated by finding the difference between the initial and final values, dividing it by the initial value, and then multiplying by 100. In this case, the initial value is $130 and the final value is $270. The difference between them is $270 - $130 = $140. Dividing $140 by $130 gives approximately 1.077. Multiplying this by 100 gives approximately 107%, which represents the percent increase from $130 to $270.
18.
Determine whether the change is an increase or decrease. Then obtain the percent of increase or decrease. Round the answer to the nearest whole percent.
old: 78 years
new: 114 years
Correct Answer
B. 46.15% increase
Explanation
The percent increase is calculated by finding the difference between the new and old values, dividing that difference by the old value, and then multiplying by 100. In this case, the difference between the new and old values is 114 - 78 = 36. Dividing 36 by 78 gives us 0.4615. Multiplying by 100 gives us 46.15%, which is the percent increase.
19.
The length of a rectangle is 6 inches more than the width.
Correct Answer
B. L = 6 + w
Explanation
The given equation "l = 6 + w" represents the length of the rectangle being 6 inches more than the width. This equation shows that if we add 6 to the width, we will get the length of the rectangle. Therefore, the equation "l = 6 + w" is the correct representation of the relationship between the length and width of the rectangle.
20.
Which answer demonstrates the distributive property?
Correct Answer
B. 4(x + 3) = 4x + 12
Explanation
The answer 4(x + 3) = 4x + 12 demonstrates the distributive property. This property states that when a number is multiplied by a sum, it can be distributed to each term within the parentheses. In this equation, the 4 is being distributed to both the x and the 3, resulting in 4x + 12 on the right side of the equation.
21.
â€¢Jim found out that after working for 9 months he had earned 6 days of vacation time. How many days will he have earned after working for two years?
Correct Answer
C. 16 days of vacation time
Explanation
If Jim earned 6 days of vacation time after working for 9 months, it means he earns 6/9 days of vacation time per month. To find out how many days he will earn after working for two years, we need to calculate the total number of months in two years, which is 24 months. Multiplying 6/9 by 24 gives us 16 days of vacation time.