Problem solving & data analysis Flashcards
The total operating costs of a monorail are paid using a combination of passenger fares and tax revenue. The farebox recovery ratio is the ratio of passenger fares to total operating costs. A monorail in one city has $69 million in operating costs per year, and uses $30 million from tax revenue. To the nearest hundredth, what is the farebox recovery ratio for the city?
We need to know the farebox recovery ratio, which is the ratio of passenger fares to total operating costs, but we do not yet know the amount of the passenger fares.
We can represent the sources of income used to pay for the operating costs with a verbal model.
passenger fares + tax revenue = operating costs
Thus:
passenger fares = operating costs - tax revenue = $69 - $30 = $39
The ratio of passenger fares to total operating costs is:
$39 / $69 = 0.5652
To the nearest hundredth, the farebox recovery ratio is 0.57
Letter count —– Number of words listed
4 letters ———- 12
5 letters ———- 49
6 letters ———- 12
7 letters ———- 9
8 letters ———- 1
On a message board, participants listed words whose letters are all in alphabetical order, such as “almost”. The table lists the number of words they listed with each letter count. What was the median letter count of the words they listed?
To find the median letter count, we need to first find the total number of words, then find the middle value.
The total number of words is:
12+49+12+9+1=83
This means the median letter count of the words is equal to the letter count of the 42nd word. In a list of 83 words ordered by letter count, 41of the words would have letter counts fewer or equal to that of the 42nd word, and 41 of the words would have letter counts greater than or equal to that of the 42nd word.
According to the table, there are 12 words with a letter count of 4 and 49 with a letter count of 5. This means if we were to write all 83 words in order of increasing letter count, the 42nd word would have a letter count of 5.
The median letter count is 5 letters.
According to a website where users review their doctors, 116 out of 119 users would recommend Dr. Gutierrez to their friends and family. If the website users are representative of Dr. Gutierrez’s 1,293 patients, about how many patients would recommend Dr. Gutierrez to their friends and family?
(Round your answer to the nearest whole number.)
We need to estimate the number of patients who would recommend Dr. Gutierrez to friends and family based on the results of a representative sample.
estimate = population * sample proportion
= 1293 * 116/119
About 1260 patients would recommend Dr. Gutierrez to their friends and family.
A donut company makes cream-filled donuts using
1/4 of dough and 1/2 tablespoon of cream per donut. The company decides to change their recipe to use 3 times the amount of cream for their “New Triple-Stuffed Donuts!” If the donut company’s new recipe uses the same amount of dough per donut, what is the ratio of dough to cream needed to make 12 triple-stuffed donuts?
Choose 1 answer:
A ] 1 : 3
B ] 1 : 6
C ] 2 : 3
D ] 1 : 2
The ratio of dough to cream for the new “triple-stuffed” recipe is
1/4 dough to 3/2 of cream.
To make a dozen triple-stuffed donuts, you need 12 times as much of the ingredients. Therefore, you need 12 * 1/4 = 3 of dough and 12 * 3/2 = 18 of cream.
So in order to make twelve triple-stuffed donuts, the ratio of dough to cream required is 3:18 = 1:6
Fabrizzio went shopping on Tuesday and decided to purchase a pair of pants that is 15% off the regular price. If he waits and buys the pants on Wednesday, he will receive an additional 5% off. What percent would Wednesday’s sale price be of the original price for the pants? Round to the nearest whole percent.
Choose 1 answer:
A ] 81%
B ] 85%
C ] 95%
D ] 105%
Let’s call the original price of the pants p. If the pants are 15% off, that means they are 85% of the original price. This means that the cost will be 0.85p, since there is no additional discount.
To determine the cost on Wednesday, we need to take off an additional 5%, so we can say that the cost is 0.95(0.85p), which is equivalent to 0.808p.
Therefore, Wednesday’s sale price would be approximately 81% of the original price.
Wednesday’s sale price would be approximately 81% of the original price.
Enzo’s favorite chocolate chip cookie recipe calls for 1 teaspoon of salt for every 2 1/4 cups of flour. He currently has 1 1/2 cups of flour in his flour jar and 4 1/2 cups of flour in a bag. If Enzo wants to use up all of his flour to make chocolate chip cookies, how many teaspoons of salt does he need?
Enzo needs 8/3 2.666 or 2.667 teaspoons of salt.
The chef has
[36] pounds of strip loin steak. The amount of weight lost from the trim on each pound is
[35\%], and
[75\%] more of the steak’s weight is lost after cooking it. How many pounds of trimmed, cooked strip loin will the chef have left to serve to the customers?
A. 5.85
B. 12.6
C. 17.55
D. 23.4
0.35 * 36 = 12.6
36 - 12.6 = 23.4
0.75 * 23.4 = 17.55
23.4 - 17.55 = 5.85
Specific gravity is the ratio, as a decimal, of the density of a substance to the density of water. Density is the ratio of the mass to the volume. The mass of
[760] gallons of fuel is
[2325] kilograms. A single gallon of water has a mass of about
3.8 kg. To the nearest tenth, what is the specific gravity of jet fuel?
Density = mass / volume
3.8 kg / 1 gal = 3.8 * kg / gal
2325 kg / 760 gal = 3.06
3.6 / 3.8 = 0.805
Approximately 0.8
In a certain high school, there were
[6] students who were not old enough to vote for every
[1] student who was old enough to vote. If there were
[840] students in the school, how many students were old enough to vote?
1 + 6 = 7
v / 840 * 1 / 7
v = 120
In the west region of the US, the ratio of densely vegetated land to sparsely vegetated land is 11:18. In the central region of the US, the ratio is 3:1. What is the difference in percentage of densely vegetated land from the west region to the central region?
A. 27.2%
B. 27.8%
C. 37.1%
D. 37.9%
Percentage =part / whole * 100%
P = 11 / 11 + 18 * 100%
PW = 37.9%
PC = “
Pc= 75%
PC - PW = 75 - 37.9
= 37.1
