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This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module is a proficiency exam to the chapter "Ratios and Rates." Each problem is accompanied with a reference link pointing back to the module that discusses the type of problem demonstrated in the question. The problems in this exam are accompanied by solutions.

Proficiency exam

( [link] ) Compare 4 cassette tapes to 7 dollars.

4 cassette tapes 7 dollars size 12{ { {"4 cassette tapes"} over {"7 dollars"} } } {}

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( [link] ) What do we call a comparison, by division, of two unlike denominate numbers?

Rate

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For problems 3 and 4, express each ratio or rate as a fraction.

( [link] ) 11 to 9

11 9 size 12{ { {"11"} over {9} } } {}

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( [link] ) 5 televisions to 2 radios

5 televisions 2 radios size 12{ { {"5 televisions"} over {"2 radios"} } } {}

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For problems 5 and 6, write each ratio or rate in the form " a to b ."

( [link] ) 8 maps 3 people size 12{ { {"8 maps"} over {"3 people"} } } {}

8 maps to 3 people

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( [link] ) 2 psychologists 75 people size 12{ { {"2 psychologists"} over {"75 people"} } } {}

two psychologists to seventy-five people

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For problems 7-9, solve each proportion.

( [link] ) 8 x = 48 90 size 12{ { {8} over {x} } = { {"48"} over {"90"} } } {}

15

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( [link] ) x 7 = 4 28 size 12{ { {x} over {7} } = { {4} over {"28"} } } {}

1

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( [link] ) 3 computers 8 students = 24   computers x   students size 12{ { {"3 computers"} over {"8 students"} } = { {"24"`"computers"} over {x" students"} } } {}

64

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( [link] ) On a map, 4 inches represents 50 miles. How many miles does 3 inches represent?

37 1 2 size 12{"37" { {1} over {2} } } {}

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( [link] ) An acid solution is composed of 6 milliliters of acid to 10 milliliters of water. How many milliliters of acid are there in an acid solution that is composed of 3 milliliters of water?

1.8

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( [link] ) The odds that a particular event will occur are 9 to 7. If the event occurs 27 times, how many times would you predict it will it not occur?

21

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For problems 13 and 14, convert each decimal to a percent.

( [link] ) 3. 7 _

377 7 9 size 12{"377" { {7} over {9} } %} {} %

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For problems 15 and 16, convert each percent to a decimal.

For problems 17-19, convert each fraction to a percent.

( [link] ) 42 5 size 12{ { {"42"} over {5} } } {}

840%

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( [link] ) 1 8 size 12{ { {1} over {8} } } {}

12.5%

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( [link] ) 800 80 size 12{ { {"800"} over {"80"} } } {}

1,000%

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For problems 20 and 21, convert each percent to a fraction.

( [link] ) 15%

3 20 size 12{ { {3} over {"20"} } } {}

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( [link] ) 4 27 size 12{ { {4} over {"27"} } } {} %

4 2, 700 or 1 675 size 12{ { {4} over {2,"700"} } " or " { {1} over {"675"} } } {}

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For problems 22-25, find each indicated quantity.

( [link] ) What is 18% of 26?

4.68

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( [link] ) 0.618 is what percent of 0.3?

206

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( [link] ) 0.1 is 1.1% of what number?

9 . 09 ¯ size 12{9 "." {overline {"09"}} } {}

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( [link] ) A salesperson makes a monthly salary of $1,000.00. He also gets a commission of 12% of his total monthly sales. If, in a particular month, he sells $5,500.00 worth of merchandise, what is his income that month?

$1,660

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Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
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