Ratio & Proportional Relationships
A tennis match was delayed because of rain. The officials were not prepared for the delay. They covered the 25ft by 20ft court with 13ft by 10ft plastic covers. How many plastic covers were needed to cover the court from the rain?
4 plastic covers
Solution:
1)Find the area of the tennis court.
2)Find out the area of one plastic cover.
3)Divide the area of the court by the area of the cover.
-3 4/5 + 9 7/10 - 2 11/20
(negative 3 and four-fifths plus nine and seven-tenths minus two and eleven-twentieths)
3 7/20 ( three and seven-twentieths)
Solution:
Which of the following statements correctly describes this expression? 2x + 4
a) four times a number plus two
b) two more than four times a number
c) four more than twice a number
d) twice a number less four
C
Solution:
Remember: Addition means more than and 2x represents multiplication, or times.
A map is designed with a scale of 1 inch for every 5 miles. If the distance between two towns is 3 inches on the map, how far apart are they?
15 miles
Solution
You can use cross product to solve for x.
1 inch/3 miles = 3 inches/x miles
15 = x
Javier will ask a survey question to determine the average number of times per month people around the United States shop for groceries. Which sample should Javier use to get results that are the most representative of the total population?
A) A random sample of 1,000 people from his town
B) A random sample of 1,000 people from his state
C)A random sample of 1,000 people from each of the 50 states
D) A random sample of 1,000 people from 5 local grocery stores
C
One third of a quart of paint covers one fourth of a basketball court. How much paint does it take to paint the entire basketball court?
1 1/3 (one and a third) quarts
Solution:
If 1/4 of a court can be covered by 1/3 of a quart of paint then to cover the entire court 4 times the amount required for covering 1/4 of a court would be required.
1/3 * 4 = 4/3 = 1 and 1/3
Jeri has had a savings account since she entered first grade. Each month of the first year she saved $1.00. Each month of the second year she saved $2.00. This pattern of adding one additional dollar each month for an entire year continued until she was saving $10.oo per month in the tenth year. How much does she have saved at the end of ten years?
$660.00
Solution:
Year1 - $12, Year 2 - $24, Year 3-$36, Year 4 - $48, Year 5 - $60, Year 6 - $72, year 7 - $84, Year 8 - $96, Year 9 - 108, Year 10 - $120
Add the totals for each year.
Which of the following expressions represents "5% of a number"?
a) 5n
b) 0.5n
c) 0.05n
d) 500n
C
Solution:
A percent is a ratio that compares a number to 100. Therefore, 5% is 5 out of 100. To convert a percent to a decimal, divide by 100: 5 divided by 100=0.05. To find 5% of a number, multiply the number times the decimal form of 5%.
A circle is divided into 4 equal sections. What is the measure of each of the angles formed at the center of the circle?
90 degrees
Solution:
A circle measures 360 degrees, so each angle formed at the center would be less than 360.
360/4 = 90 degrees
Elam surveyed 120 registered voters at random out of a total of 12, 600 registered voters in his town. He asked them who they planned to vote for in the upcoming election.
Number of Expected Votes
Ms. Gibson Ms. Reynolds
45 75
Based on the results of Elam's first survey, what is the total number of registered voters expected to vote for Ms. Gibson in the upcoming election?
4725
Solution
Set up a proportional relationship.
Number of expected votes for Ms. Gibson/total number of expected votes = total number of registered voters expected to vote for Ms. Gibson/ total number of registered voters
45/120 = x/12,600
120x = 567000
x = 4,725
If the ratio of the length of a rectangle to its width is 3 to 2, what is the length of a rectangle whose width is 4 inches?
6 in.
Solution:
Set up a proportion.
3/2 = x/4
2x = 12
x = 6
For what numbers will this statement be true?: t - (w) = t + (-w)
a) All positive numbers only
b) All positive integers only
c) All positive and negative integers, but not 0
d) All real numbers
D
Solution:
The statement says that subtracting a number is the same as adding the opposite of that number. This is true for all real numbers.
Ja-Mes is 4 years older than his brother Mickel. In two years, Ja-Mes will be twice Mickel's age. How old are they now?
Ja-Mes is 6 and Mickel is 2
Solution:
Now: Mickel's age = x, Ja-Mes' age = x + 4
In 2 years: Mickel's age = x + 2, Ja-Mes' age = x + 4 + 2 = x + 6
It is given that, in 2 years, Ja-Mes' ge is twice Mickel's age. Therefore, we have x + 6 = 2(x + 2)
x + 6 = 2x + 4
6 = x + 4 = Ja-Mes
2 = x = Mickel
A circular frisbee has a circumference of 15.2 inches. What is the area of this frisbee? Use 3.14 for pi. Round to the nearest whole number if needed.
18 square inches
Solution
Area = pi * radius squared
Circumference = pi * diameter
If the circumference is 15.2, then if you divided by pi, you can find the diameter (4.8407). Then the radius =2.42. Therefore the area is pi(2.42) ^2
Area = 18 square inches (rounded to nearest whole number)
The owner of a sports stadium decides to give prizes to people who attend a game. When people enter the stadium, each person will received a hat or a key ring. The probability of a person receiving each prize is listed.
0.9 for a key ring
1/10 for a hat
Which statement about the probabilities shown is true?
A) A person is likely to receive a hate because the probability is close to 1.
B) A person is unlikely to receive a hat because the probability is close to 1.
C) A person is likely to receive a key ring because the probability is close to 1.
D) A person is unlikely to receive a key ring because the probability is close to 1.
C
Suppose you are buying pizzas for a party. An equation that represents the cost (y) in dollars for x number of pizzas is y=18x.
Does the equation y=18x represent a proportional relationship? (Select all that are true.)
A) No, the graph of the equation does not pass through the origin.
B) Yes, the graph of the equation is a straight line.
C) Yes, the graph of the equation passes through the origin.
D) No, the graph of the equation is not a straight line.
B & C
Solution:
One can check whether or not an equation of a line represents a proportional relationship by observing whether the equation represents a straight line and whether the line passes through the origin.
Micah bought pizza and soda for herself and four of her friends. The pizza was $17.49, and the 5 sodas were $1.19 each. If the pizza is sliced into 10 equal slices and each person eats 2 slices and drinks one soda, what is the cost to each person?
$4.69
Solution:
The pizza was equally divided so each person's cost for pizza is $17.49 divided by 5 = $3.50. Soda was $1.19 each. Add to find the total cost for each person. $3.50 + $1.19 = $4.69
Melanie has $35.00 in her savings account and does cleaning in a neighbor's house for $15.00 per week. Sue has no money save, but is mowing lawns at $20.00 each. If Sue mows 1 lawn per week, how long will it take her to catch up with Melanie?
a) 5 weeks
b) 6 weeks
c) 7 weeks
d) 8 weeks
C
Solution:
Let n= number of weeks of work for Sue to catch up with Melanie
35 + 15n = 20n
35 = 5n
7 = n
Find the volume of a right pyramid that has a height of 14 inches and a base area of 25 square inches. Round your answer to the nearest whole number.
117 cubic inches
Solution
The formula for volume of a right pyramid is 1/3 of the product of the height and the base area. Therefore, 1/3(14*25) = 116.666...
Rounded to the nearest whole number is 117 cubic inches
Maya scored 7, 9, 2, 6, 15 and 15 points in 6 basketball games. Find the mean, median and mode scores for all the games.
Mean = 9, median = 8 and mode = 15
Solution
Mean is the average, median is the middle-number when data is arranged numerically, and the mode is the number that appears most often
When Frank buys three packs of pens, he knows he has 36 pens. When he buys five packs, he knows he has 60 pens. What is the constant of proportionality between the number of packs and the number of pens?
12 pens per pack
Solution:Divide the number of pens by the number of packs for either pair of data.
Which of the following numbers is divisible by 3?
a) 459,732
b) 129,682
c) 1,999,000
d) 5,684,722
A
Solution:
If the sum of the digits is divisible by 3, the the number is divisible by 3. The sum of the digits of 459,732 is 30 which is divisible by 3. Therefore, 459,732 is divisible by 3.
The initial cost to rent a bike is $5. Each hours the bike is rented costs $2. Lis is going to rent a bike and can spend at most $17. Write and solve an inequality to find how long she can rent the bike.
5 + 2x is less than or equal to 17
x = 6 hrs
Solution:
Write the inequality to be: 5 + 2x is less than or equal to 17. Subtract 5 from each side and divide by 2 to get 6. So, Liz can rent a bike almost for 6 hours.
The sum of the measures of a pair of vertical angles, angle a and angle b, is 155 degrees. What is the measure of angle b?
77.5 degrees
Solution
Vertical angles are congruent angles formed by two intersecting lines. Angle a and angle b are equal in measure. To find the value of angle b, divide 155 by 2. The quotient is the value of angle b.
Two friends both happened to buy new trucks from the same manufacturer in the same week. The manufacturer offers 4 models of trucks in 6 different colors. What is the probability that the two friends happened to buy the same model and color of truck?
a) 1 out of 10
b) 1 out of 14
c) 1 out of 15
d) 1 out of 24
D
Solution
After the first person has chosen the truck, the probability that the second person choose the same model is 1 in 4 and he (second person) choose the same color is 1 in 6. Therefore, the probability that the second person choose the same model and the same color as the first person =
1/4 * 1/6 = 1/24