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Proficiency Exam

Module by: Wade Ellis, Denny Burzynski. E-mail the authorsEdited By: Math Editors

Summary: 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

Exercise 1

((Reference)) Compare 4 cassette tapes to 7 dollars.

Solution

4 cassette tapes7 dollars4 cassette tapes7 dollars size 12{ { {"4 cassette tapes"} over {"7 dollars"} } } {}

Exercise 2

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

Solution

Rate

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

Exercise 3

((Reference)) 11 to 9

Solution

119119 size 12{ { {"11"} over {9} } } {}

Exercise 4

((Reference)) 5 televisions to 2 radios

Solution

5 televisions2 radios5 televisions2 radios size 12{ { {"5 televisions"} over {"2 radios"} } } {}

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

Exercise 5

((Reference)) 8 maps3 people8 maps3 people size 12{ { {"8 maps"} over {"3 people"} } } {}

Solution

8 maps to 3 people

Exercise 6

((Reference)) 2 psychologists75 people2 psychologists75 people size 12{ { {"2 psychologists"} over {"75 people"} } } {}

Solution

two psychologists to seventy-five people

For problems 7-9, solve each proportion.

Exercise 7

((Reference)) 8x=48908x=4890 size 12{ { {8} over {x} } = { {"48"} over {"90"} } } {}

Solution

15

Exercise 8

((Reference)) x7=428x7=428 size 12{ { {x} over {7} } = { {4} over {"28"} } } {}

Solution

1

Exercise 9

((Reference)) 3 computers8 students=24  computersx  students3 computers8 students=24  computersx  students size 12{ { {"3 computers"} over {"8 students"} } = { {"24"`"computers"} over {x" students"} } } {}

Solution

64

Exercise 10

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

Solution

37123712 size 12{"37" { {1} over {2} } } {}

Exercise 11

((Reference)) 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?

Solution

1.8

Exercise 12

((Reference)) 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?

Solution

21

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

Exercise 14

((Reference)) 3. 7 _ 3. 7 _

Solution

3777937779 size 12{"377" { {7} over {9} } %} {}%

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

Exercise 15

Exercise 16

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

Exercise 17

((Reference)) 425425 size 12{ { {"42"} over {5} } } {}

Solution

840%

Exercise 18

((Reference)) 1818 size 12{ { {1} over {8} } } {}

Solution

12.5%

Exercise 19

((Reference)) 8008080080 size 12{ { {"800"} over {"80"} } } {}

Solution

1,000%

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

Exercise 20

((Reference)) 15%

Solution

320320 size 12{ { {3} over {"20"} } } {}

Exercise 21

((Reference)) 427427 size 12{ { {4} over {"27"} } } {} %

Solution

42,700 or 167542,700 or 1675 size 12{ { {4} over {2,"700"} } " or " { {1} over {"675"} } } {}

For problems 22-25, find each indicated quantity.

Exercise 22

((Reference)) What is 18% of 26?

Solution

4.68

Exercise 23

((Reference)) 0.618 is what percent of 0.3?

Solution

206

Exercise 24

((Reference)) 0.1 is 1.1% of what number?

Solution

9.09¯9.09¯ size 12{9 "." {overline {"09"}} } {}

Exercise 25

((Reference)) 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?

Solution

$1,660

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