How to find a ratio - SSAT Upper Level Quantitative
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In a zoo with 
animals, the ratio of mammals to reptiles to birds is 
. How many birds does the zoo have?
In a zoo with
Let 
be the number of mammals,
be the number of reptiles, and 
be the number of birds.
Since the zoo has 
animals,
Because we want the number of birds, we need to find the value of 
.
Let
Since the zoo has
Because we want the number of birds, we need to find the value of
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John and Michela are business partners who agreed to split profits at a ratio of 2:3, with Michela taking the larger share. If their business made 
in the first year, how much money did Michela make?
John and Michela are business partners who agreed to split profits at a ratio of 2:3, with Michela taking the larger share. If their business made
Let 
be the amount John takes home and 
be the amount Michela takes home.
Since their business made 
,
We want to know how much Michela made so we need to find the value of 
.
Let
Since their business made
We want to know how much Michela made so we need to find the value of
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A barn has 
geese, 
ducks, and 
chickens. What is the ratio of geese to chickens?
A barn has
First, add up the total number of ducks, geese, and chickens.
Now, write the fraction of these animals that are geese and the fraction of these animals that are chickens.
Now, since we want the ratio of geese to chickens, we write the fractions as thus:
Divide and simplify the resulting fraction to find the ratio.
First, add up the total number of ducks, geese, and chickens.
Now, write the fraction of these animals that are geese and the fraction of these animals that are chickens.
Now, since we want the ratio of geese to chickens, we write the fractions as thus:
Divide and simplify the resulting fraction to find the ratio.
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If 
pounds of chicken cost 
, how much does 
pounds of chicken cost?
If
There is more than one way to solve this problem. You can either figure out how much the chicken costs per pound and multiply that cost by three pounds, or you can set up a proportion and solve for the cost of three pounds of chicken that way.
- Solving the Problem Using Cost per Pound
First, find how much the chicken costs per pound.
Since chicken costs 
per pound, multiply this by the number of pounds we need to get the cost.
pounds of chicken cost 
.
- Solving the Problem Using a Proportion
You can set up a proportion to figure out how much 
pounds of chicken costs:
Cross multiply:
Solve for 
, the cost of 
pounds of chicken:
There is more than one way to solve this problem. You can either figure out how much the chicken costs per pound and multiply that cost by three pounds, or you can set up a proportion and solve for the cost of three pounds of chicken that way.
- Solving the Problem Using Cost per Pound
First, find how much the chicken costs per pound.
Since chicken costs
- Solving the Problem Using a Proportion
You can set up a proportion to figure out how much
Cross multiply:
Solve for
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In a class of 
students, the ratio of freshmen to sophomores to juniors is 
. How many juniors are in the class?
In a class of
Let 
be the number of freshmen, 
be the number of sophomores, and 
be the number of juniors.
Now, since we have 
students,
Since we want to find the number of juniors, we need to find the value of 
.
Let
Now, since we have
Since we want to find the number of juniors, we need to find the value of
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The angles in a triangle are in the ratio 
. What is the angle measurement of the largest angle?
The angles in a triangle are in the ratio
Let 
be the values of the angles.
Since all the angles in a triangle need to add up to 
,
Because we want the value of the largest angle, we need to find the value of 
.
Let
Since all the angles in a triangle need to add up to
Because we want the value of the largest angle, we need to find the value of
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The angles in a triangle have a ratio of 
. What is the measurement of the smallest angle?
The angles in a triangle have a ratio of
Let 
be the values of the angles.
Since there are 
degrees in a triangle,
Since we want the value of the smallest angle, find the value of 
.
Let
Since there are
Since we want the value of the smallest angle, find the value of
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In a high school of 
students, the ratio of freshmen to sophomores to juniors to seniors is 
. How many juniors does this high school have?
In a high school of
Let 
be the number of freshmen, 
be the number of sophomores, 
be the number of juniors, and 
be the number of seniors.
Because the high school has 
students,
Since we want to find out how many juniors there are, we need the value of 
.
Let
Because the high school has
Since we want to find out how many juniors there are, we need the value of
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In a factory, there are 
glass bottles. If the ratio of red bottles to blue bottles is 
, how many more blue bottles than red bottles are there?
In a factory, there are
First, find the number of red bottles and blue bottles.
Let 
be the number of red bottles and 
be the number of blue bottles. Since there is a total of 
bottles at the factory,
There are 
red bottles. Find the value of 
to find the number of blue bottles.
Now, because the question wants to find how many more blue bottles than red bottles there are, subtract the number of red bottles from the number of blue bottles.
First, find the number of red bottles and blue bottles.
Let
There are
Now, because the question wants to find how many more blue bottles than red bottles there are, subtract the number of red bottles from the number of blue bottles.
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The ratio of offensive players to defensive players on a football team is 
. If there are 
players on the team, how many offensive players are there?
The ratio of offensive players to defensive players on a football team is
Let 
be the number of offensive players and 
be the number of defensive players.
Since there is a total of 
players on the team,
We need to find the number of offensive players, so we will need to find the value of 
.
Let
Since there is a total of
We need to find the number of offensive players, so we will need to find the value of
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In a high school, the ratio of freshmen to seniors is 
. If there are 
seniors, how many freshmen are there?
In a high school, the ratio of freshmen to seniors is
Set up the following proportion, with 
being the number of freshmen.
Now, cross-multiply and solve for 
.
Set up the following proportion, with
Now, cross-multiply and solve for
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On a beach, the ratio of crabs to seagulls is 
. If there are 
crabs and seagulls on the beach, how many crabs are there?
On a beach, the ratio of crabs to seagulls is
Let 
be the number of crabs and 
be the number of seagulls.
Since there are 
crabs and seagulls on the beach,
Because the question asks for the number of crabs, we need to find the value of 
.
Let
Since there are
Because the question asks for the number of crabs, we need to find the value of
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There are 
boys and 
girls at a playground. What is the ratio of boys to girls?
There are
Write the numbers of boys and girls as a fraction, then simplify.
can also be written as 
Write the numbers of boys and girls as a fraction, then simplify.
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At a high school, there are 
freshmen, 
sophomores, 
juniors, and 
seniors. What is the ratio of seniors to freshmen?
At a high school, there are
Write the number of seniors and numbers of freshmen as a fraction:
That fraction is equivalent to 
.
Write the number of seniors and numbers of freshmen as a fraction:
That fraction is equivalent to
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A popular word game uses one hundred tiles, each of which is marked with a letter or a blank. The distribution of the tiles is shown above, with each letter paired with the number of tiles marked with that letter. Notice that there are two blank tiles.
If the tiles marked with an "E" are removed, and the rest are placed in a box, then what is the ratio of consonant tiles to vowel tiles in the box?
Note: for purposes of this problem, "Y" is considered a consonant.
A popular word game uses one hundred tiles, each of which is marked with a letter or a blank. The distribution of the tiles is shown above, with each letter paired with the number of tiles marked with that letter. Notice that there are two blank tiles.
If the tiles marked with an "E" are removed, and the rest are placed in a box, then what is the ratio of consonant tiles to vowel tiles in the box?
Note: for purposes of this problem, "Y" is considered a consonant.
Out of the 100 tiles, there are nine "A" tiles, twelve "E" tiles, nine "I" tiles, eight "O" tiles, and four "U" tiles.
If the "E" tiles are removed, there will be
vowel tiles.
The number of consonant tiles can most easily be found by adding the number of vowel tiles and blanks:
.
The rest of the tiles are consonant tiles; subtract from 100 to get
of them.
Therefore, the ratio of consonant tiles to vowel tiles in the box after removing the "E's" is
- that is, a 28 to 15 ratio.
Out of the 100 tiles, there are nine "A" tiles, twelve "E" tiles, nine "I" tiles, eight "O" tiles, and four "U" tiles.
If the "E" tiles are removed, there will be
The number of consonant tiles can most easily be found by adding the number of vowel tiles and blanks:
The rest of the tiles are consonant tiles; subtract from 100 to get
Therefore, the ratio of consonant tiles to vowel tiles in the box after removing the "E's" is
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A barn has geese, ducks, and chickens. What is the ratio of geese to chickens?
A barn has
First, add up the total number of ducks, geese, and chickens.
Now, write the fraction of these animals that are geese and the fraction of these animals that are chickens.
Now, since we want the ratio of geese to chickens, we write the fractions as thus:
Divide and simplify the resulting fraction to find the ratio.
First, add up the total number of ducks, geese, and chickens.
Now, write the fraction of these animals that are geese and the fraction of these animals that are chickens.
Now, since we want the ratio of geese to chickens, we write the fractions as thus:
Divide and simplify the resulting fraction to find the ratio.
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If pounds of chicken cost , how much does pounds of chicken cost?
If
There is more than one way to solve this problem. You can either figure out how much the chicken costs per pound and multiply that cost by three pounds, or you can set up a proportion and solve for the cost of three pounds of chicken that way.
- Solving the Problem Using Cost per Pound
First, find how much the chicken costs per pound.
Since chicken costs per pound, multiply this by the number of pounds we need to get the cost.
pounds of chicken cost .
- Solving the Problem Using a Proportion
You can set up a proportion to figure out how much pounds of chicken costs:
Cross multiply:
Solve for , the cost of pounds of chicken:
There is more than one way to solve this problem. You can either figure out how much the chicken costs per pound and multiply that cost by three pounds, or you can set up a proportion and solve for the cost of three pounds of chicken that way.
- Solving the Problem Using Cost per Pound
First, find how much the chicken costs per pound.
Since chicken costs
- Solving the Problem Using a Proportion
You can set up a proportion to figure out how much
Cross multiply:
Solve for
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In a class of students, the ratio of freshmen to sophomores to juniors is . How many juniors are in the class?
In a class of
Let be the number of freshmen, be the number of sophomores, and be the number of juniors.
Now, since we have students,
Since we want to find the number of juniors, we need to find the value of .
Let
Now, since we have
Since we want to find the number of juniors, we need to find the value of
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The angles in a triangle are in the ratio . What is the angle measurement of the largest angle?
The angles in a triangle are in the ratio
Let be the values of the angles.
Since all the angles in a triangle need to add up to ,
Because we want the value of the largest angle, we need to find the value of .
Let
Since all the angles in a triangle need to add up to
Because we want the value of the largest angle, we need to find the value of
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In a zoo with animals, the ratio of mammals to reptiles to birds is . How many birds does the zoo have?
In a zoo with
Let be the number of mammals, be the number of reptiles, and be the number of birds.
Since the zoo has animals,
Because we want the number of birds, we need to find the value of .
Let
Since the zoo has
Because we want the number of birds, we need to find the value of
Compare your answer with the correct one above