SAT Math › How to find a ratio
Two cars were traveling 630 miles. Car A traveled an average speed of 70 miles per hour. If car B traveled 90 miles an hour, how many miles had car A traveled when car B arrived at the destination?
700
140
630
490
We first divide 630 miles by 90 miles per hour to get the amount of time it took car B to reach the destination, giving us 7 hours. We then multiply 7 hours by car A’s average speed and we get 490 miles.
In the reptile house at the zoo, the ratio of snakes to lizards is 3 to 5. After the zoo adds 15 more snakes to the exhibit, the ratio changes to 4 to 5. How many lizards are in the reptile house?
50
75
90
120
135
In order to maintain a proportion, each value in the ratio must be multiplied by the same value:
Before and after the snakes arrive, the number of lizards stays constant.
Before new snakes — Snakes : Lizards = 3_x_ : 5_x_
After new snakes — Snakes : Lizards = 4_x_ : 5_x_
Before the new snakes arrive, there are 3_x_ snakes. After the 15 snakes are added, there are 4_x_ snakes. Therefore, 3_x_ + 15 = 4_x_. Solving for x gives x = 15.
There are 5x lizards, or 5(15) = 75 lizards.
The first term in a sequence is m. If every term thereafter is 5 greater than 1/10 of the preceding term, and m≠0, what is the ratio of the second term to the first term?
(m+5)/10
(m+10)/5
(m+10)/50m
(m+50)/10m
The first term is m, so the second term is m/10+5 or (m+50)/10. When we take the ratio of the second term to the first term, we get (((m+50)/10))/m, which is ((m+50)/10)(1/m), or (m+50)/10m.
The ratio of the number of financial employees who remained in the same role for 2 to 9 years to the number of construction employees who remained in the same role for 0 to 4 years is closest to which of the following?
For this problem, we need to find the number of employees who fall into the categories described, keeping in mind that multiple portions of the pie chart must be accommodated for. Then, we can fit them into a ratio:
For the "2 to 9 years" portion of the financial industry, include
(0.2 + 0.18)(12,000,000) = 4,560,000 workers.
For the "0 to 4 years" portion of the construction industry, include
(0.15 + 0.2)(8,000,000) = 2,800,000 workers.
Now divide and simplify to find the ratio:
4,560,000/2,800,000 = 8/5.
If the ratio of q to r is 3:5 and the ratio of r to s is 10:7, what is the ratio of q to s?
1:7
6:7
7:3
7:5
3:7
Multiply the ratios. (q/r)(r/s)= q/s. (3/5) * (10/7)= 6:7.
STUDENT ATHLETES WHO USE STEROIDS | |||
---|---|---|---|
MEN | WOMEN | TOTAL | |
BASKETBALL | A | B | C |
SOCCER | D | E | F |
TOTAL | G | H | I |
In the table above, each letter represents the number of students in each category. Which of the following must be equal to I?
A+D+G
A+D
G+H
A+B
Since G is the total number of male athletes that use steroids and H is the total number of female athletes that use steroids, the sum of the two is equal to I, which is the total number of all students using steroids.
A particular ball always bounces back to 2/5 of the height of its previous bounce after being dropped. After the first bounce it reaches a height of 175 inches. Approximately how high (in inches) will it reach after its fifth bounce?
11.2
4.5
20
14
The first bounce reaches a height of 175. The second bounce will equal 175 multiplied by 2/5 or 70. Repeat this process. You will get the data below. 4.48 is rounded to 4.5.
A gallon contains 8 pints. Each pint contains 2 cups. How many cups are in a 10-gallon jug of water?
160
80
26
20
220
Find the number of cups in a gallon, then calculate cups in 10 gallons.
If 8 pints = 1 gallon, then 16 cups = 1 gallon
16 cups * 10 gallons = 160 cups
A bag contains 240 marbles that are either red, blue, or green. The ratio of red to blue to green marbles is 5 : 2 : 1. If one-third of the red marbles and two-thirds of the green marbles are removed, what fraction of the remaining marbles in the bag will be blue?
1/3
6/17
1/2
7/18
6/13
First, we need to figure out how many red, blue, and green marbles are in the bag before any are removed. Let 5x represent the number of red marbles. Because the marbles are in a ratio of 5 : 2 : 1, then if there are 5x red marbles, there are 2x blue, and 1x green marbles. If we add up all of the marbles, we will get the total number of marbles, which is 240.
5x + 2x + 1x = 240
8x = 240
x = 30
Because the number of red marbles is 5x, there are 5(30), or 150 red marbles. There are 2(30), or 60 blue marbles, and there are 1(30), or 30 green marbles.
So, the bag originally contains 150 red, 60 blue, and 30 green marbles. We are then told that one-third of the red marbles is removed. Because one-third of 150 is 50, there would be 100 red marbles remaining. Next, two-thirds of the green marbles are removed. Because (2/3)(30) = 20, there would be 10 green marbles left after 20 are removed.
To summarize, after the marbles are removed, there are 100 red, 60 blue, and 10 green marbles. The question asks us for the fraction of blue marbles in the bag after the marbles are removed. This means there would be 60 blue marbles out of the 170 left in the bag. The fraction of blue marbles would therefore be 60/170, which simplifies to 6/17.
The answer is 6/17.
A cafeteria with 40 tables can sit 600 people. Some tables can sit 10 people and some can sit 20 people. What is the ratio of the number of 10-person tables to the number of 20-person tables?
1:1
2:1
1:2
4:1
1:4
Let x be the number of 10-person tables, and y be the number of 20-person tables. Since there are 40 tables in the cafeteria, x + y = 40. 10_x_ represents the number of people sitting at 10-person tables, and 20_y_ represents the number of people sitting at 20-person tables. Since the cafeteria can seat 600 people, 10_x_ + 20_y_ = 600. Now we have 2 equations and 2 unknowns, and can solve the system. To do this, multiply the first equation by 10 and subtract it from the second equation. This yields 0_x_ + 10_y_ = 200; solving for y tells us there are 20 tables that seat 20 people. Since x + y = 40, x = 20, so there are 20 tables that seat 10 people. The ratio of x:y is therefore 1:1.