How to find a ratio a1 - ACT Math
Card 0 of 11
Jeff went to a bookstore where science books cost $10.00 each and comic books cost $5.50 each. If Jeff bought twice as many comic books as science books, and spent a total of $42.00, how many comic books did he buy?
Jeff went to a bookstore where science books cost $10.00 each and comic books cost $5.50 each. If Jeff bought twice as many comic books as science books, and spent a total of $42.00, how many comic books did he buy?
Assign a variable to science books since everything in the question can be written in terms of science books.
Write an expression for the phrase "twice as many comic books as science books."
To create an equation for the cost of the books, we can write the following:
Substitute in the known values and variables.
Jeff purchased 2 science books and 4 comic books.
Assign a variable to science books since everything in the question can be written in terms of science books.
Write an expression for the phrase "twice as many comic books as science books."
To create an equation for the cost of the books, we can write the following:
Substitute in the known values and variables.
Jeff purchased 2 science books and 4 comic books.
Compare your answer with the correct one above
The ratio of 
to 
is 4 to 9, and the ratio of 
to 
is 5 to 6. What is the ratio of 
to 
?
The ratio of 
Using the given information we can generate the following two proportions:
and 
Next, cross-multiply each proportion to come up with the following two equations:
and 
Each equation shares a term with the 
variable. We need to make this variable equal in both equations to continue. Multiply the first equation by a factor of 3 and the second by a factor of 2, so that the 
terms are equivalent. Let's start with the first equation.
Now, we will perform a similar operation on the second equation.
Now, we can set these equations equal to one another.
Drop the equivalent 
terms.
The proportion then becomes the following:
or 
Using the given information we can generate the following two proportions:
Next, cross-multiply each proportion to come up with the following two equations:
Each equation shares a term with the 
Now, we will perform a similar operation on the second equation.
Now, we can set these equations equal to one another.
Drop the equivalent 
The proportion then becomes the following:
Compare your answer with the correct one above
On her birthday in 2013, Molly was three times older than Steve. On her birthday in 2016, Molly was 2 times older than Steve. How old was Steve on Molly's birthday in 2013?
On her birthday in 2013, Molly was three times older than Steve. On her birthday in 2016, Molly was 2 times older than Steve. How old was Steve on Molly's birthday in 2013?
First, let's assign variables to the names of the individuals to represent their age in 2013.
In 2013, Molly was three times older than Steve; therefore, we can write the following expression:
We are also told that in 2016, Molly will be two times older than Steve; thus, we can write another expression:
.
We can then substitute 
in for 
in the second equation to arrive at the following:
First, let's assign variables to the names of the individuals to represent their age in 2013.
In 2013, Molly was three times older than Steve; therefore, we can write the following expression:
We are also told that in 2016, Molly will be two times older than Steve; thus, we can write another expression:
We can then substitute 
Compare your answer with the correct one above
The ratio of a to b is 9:2, and the ratio of c to b is 5:3. What is the ratio of a to c?
The ratio of a to b is 9:2, and the ratio of c to b is 5:3. What is the ratio of a to c?
Set up the proportions a/b = 9/2 and c/b = 5/3 and cross multiply.
2a = 9b and 3c = 5b.
Next, substitute the b’s in order to express a and c in terms of each other.
10a = 45b and 27c = 45b --> 10a = 27c
Lastly, reverse cross multiply to get a and c back into a proportion.
a/c = 27/10
Set up the proportions a/b = 9/2 and c/b = 5/3 and cross multiply.
2a = 9b and 3c = 5b.
Next, substitute the b’s in order to express a and c in terms of each other.
10a = 45b and 27c = 45b --> 10a = 27c
Lastly, reverse cross multiply to get a and c back into a proportion.
a/c = 27/10
Compare your answer with the correct one above
Joe needs to repair the roof of his house. He finds two companies that can complete the job. Company A charges an initial cost of $120, plus $15 per hour of labor, while Company B charges an initial cost of $95, plus $20 per hour of labor. After how many hours of labor does Company A cost less than Company B to repair the roof?
Joe needs to repair the roof of his house. He finds two companies that can complete the job. Company A charges an initial cost of $120, plus $15 per hour of labor, while Company B charges an initial cost of $95, plus $20 per hour of labor. After how many hours of labor does Company A cost less than Company B to repair the roof?
In order to solve this problem, create an equation that summarizes the roof repair cost for each company. Begin by composing a formula for Company A, which charges 120 dollars upfront and 15 dollars per hour of labor.
Now, Company B charges 95 dollars upfront and 20 dollars per hour of labor. We can write the following equation:
The question asks us to find how many hours of labor that a repair must take in order for Company A to be cheaper than Company B. In other words, we need to compose an inequality in which the cost of Company A is less than the cost of Company B. We will substitute the variable 
for hours and solve.
Subtract 
from each side of the inequality.
Subtract 95 from both sides of the inequality.
Divide both sides of the inequality by 5.
If the repair will take more than 5 hours, Company A will be cheaper.
In order to solve this problem, create an equation that summarizes the roof repair cost for each company. Begin by composing a formula for Company A, which charges 120 dollars upfront and 15 dollars per hour of labor.
Now, Company B charges 95 dollars upfront and 20 dollars per hour of labor. We can write the following equation:
The question asks us to find how many hours of labor that a repair must take in order for Company A to be cheaper than Company B. In other words, we need to compose an inequality in which the cost of Company A is less than the cost of Company B. We will substitute the variable 
Subtract 
Subtract 95 from both sides of the inequality.
Divide both sides of the inequality by 5.
If the repair will take more than 5 hours, Company A will be cheaper.
Compare your answer with the correct one above
There is a shipment of 50 radios; 5 of them are defective; what is the ratio of non-defective to defective?
There is a shipment of 50 radios; 5 of them are defective; what is the ratio of non-defective to defective?
Since there are 5 defective radios, there are 45 nondefective radios; therefore, the ratio of non-defective to defective is 45 : 5, or 9 : 1.
Since there are 5 defective radios, there are 45 nondefective radios; therefore, the ratio of non-defective to defective is 45 : 5, or 9 : 1.
Compare your answer with the correct one above
The ratio of 
to 
is 
to 
, while the ratio of 
to 
is 
to 
.
What is the ratio of 
to 
?
The ratio of
What is the ratio of
Since the ratios are fixed, regardless of the actual values of 
, 
, or 
, we can let 
and 
In order to convert to a form where we can relate 
to 
, we must set the coefficient of 
of each ratio equal such that the ratio can be transferred. This is done most easily by finding a common multiple of 
and 
(the ratio of 
to 
and 
, respectively) which is 
Thus, we now have 
and 
.
Setting the 
values equal, we get 
, or a ratio of 
Since the ratios are fixed, regardless of the actual values of
In order to convert to a form where we can relate
Thus, we now have
Setting the
Compare your answer with the correct one above
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?
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.
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.
Compare your answer with the correct one above
A bag contains 3 green marbles, 5 red marbles, and 9 blue marbles.
What is the ratio of green marbles to blue marbles?
A bag contains 3 green marbles, 5 red marbles, and 9 blue marbles.
What is the ratio of green marbles to blue marbles?
The ratio of green to blue is 
.
Without simplifying, the ratio of green to blue is 
(order does matter).
Since 3 and 9 are both divisible by 3, this ratio can be simplified to 
.
The ratio of green to blue is
Without simplifying, the ratio of green to blue is
Since 3 and 9 are both divisible by 3, this ratio can be simplified to
Compare your answer with the correct one above
A small company's workforce consists of store employees, store managers, and corporate managers in the ratio 10:3:1. How many employees are either corporate managers or store managers if the company has a total of 
employees?
A small company's workforce consists of store employees, store managers, and corporate managers in the ratio 10:3:1. How many employees are either corporate managers or store managers if the company has a total of
Let 
be the number of store employees, 
the number of store managers, and 
the number of corporate managers.
, so the number of store employees is 
.
, so the number of store managers is 
.
, so the number of corporate managers is 
.
Therefore, the number of employees who are either store managers or corporate managers is 
.
Let
Therefore, the number of employees who are either store managers or corporate managers is
Compare your answer with the correct one above
There are thirty cups and fifteen saucers on a shelf. If three saucers are broken and five cups are added, what will be the ratio of cups to saucers?
There are thirty cups and fifteen saucers on a shelf. If three saucers are broken and five cups are added, what will be the ratio of cups to saucers?
First, begin by calculating the total number of each item that there will be at the end of the process.
Cups: 
Saucers: 
The ratio of cups to saucers will thus be:
First, begin by calculating the total number of each item that there will be at the end of the process.
Cups:
Saucers:
The ratio of cups to saucers will thus be:
Compare your answer with the correct one above