Proportion / Ratio / Rate
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SSAT Upper Level Quantitative › Proportion / Ratio / Rate
Julie can read pages in
minutes. How long, in minutes, would it take Julie to read a book that had
pages?
Explanation
First, figure out how long it takes Julie to read 1 page.
It takes Julie minutes to read one page. Now, multiply this by the number of pages she needs to read to find out how long it will take her.
It will take Julie minutes to read
pages.
Express as a ratio.
Explanation
Ratios take the form of numerator:deminator when in colon form.
In a high school, the ratio of freshmen to seniors is . If there are
seniors, how many freshmen are there?
Explanation
Set up the following proportion, with being the number of freshmen.
Now, cross-multiply and solve for .
In a high school, the ratio of freshmen to seniors is . If there are
seniors, how many freshmen are there?
Explanation
Set up the following proportion, with being the number of freshmen.
Now, cross-multiply and solve for .
Express as a ratio.
Explanation
Ratios take the form of numerator:deminator when in colon form.
Julie can read pages in
minutes. How long, in minutes, would it take Julie to read a book that had
pages?
Explanation
First, figure out how long it takes Julie to read 1 page.
It takes Julie minutes to read one page. Now, multiply this by the number of pages she needs to read to find out how long it will take her.
It will take Julie minutes to read
pages.
In a biology class, students are freshmen,
students are sophomores, and
students are juniors. What is the ratio of sophomores to freshmen in the class?
Explanation
The ratio of sophomores to freshmen in the class can be expressed by the fraction .
Now, simplify this fraction.
That fraction can also be expressed as .
In a biology class, students are freshmen,
students are sophomores, and
students are juniors. What is the ratio of sophomores to freshmen in the class?
Explanation
The ratio of sophomores to freshmen in the class can be expressed by the fraction .
Now, simplify this fraction.
That fraction can also be expressed as .
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.
Explanation
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.
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.
Explanation
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.