Algebra II : Setting Up Equations

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #439 : Basic Single Variable Algebra

A textbook says that, on average, a moose that is \displaystyle 6.9ft tall will be \displaystyle 9.7ft long.  Using that proportion, which equation would you use to figure out how long a \displaystyle 5.8ft tall moose is?

Possible Answers:

\displaystyle \frac{length}{6.9ft}=\frac{9.7ft}{5.8ft}

\displaystyle length=\frac{9.7ft}{6.9ft\cdot 5.8ft}

\displaystyle length\cdot 5.8ft=9.7ft\cdot5.8ft

\displaystyle \frac{length}{5.8ft}=\frac{9.7ft}{6.9ft}

\displaystyle \frac{length}{9.7ft}=\frac{5.7ft}{6.9ft}

Correct answer:

\displaystyle \frac{length}{5.8ft}=\frac{9.7ft}{6.9ft}

Explanation:

Because this is a question about proportions, we know there's going to be one number divided by another number.  First, we're going to group our textbook length and height together:

\displaystyle \frac{9.7ft}{6.9ft}

As you can see, we choose to put the length of the moose in the numerator.  It doesn't matter if we put it in the numerator or the denominator yet.  When we group the height of the visible moose and it's length, we're going to put the length in the numerator because that's what we did for the textbook length:

\displaystyle \frac{length}{5.8ft}

Had we put the lengths in the denominators, that would have been fine (we just would have had an extra step when solving the problem).  Now we set our proportions equal to each other to get a final equation of:

\displaystyle \frac{length}{5.8ft}=\frac{9.7ft}{6.9ft}

Example Question #91 : Equations

A slice of pizza has \displaystyle 4 pieces of pepperoni on it, and a full pizza has \displaystyle 8 slices.  If you order a pizza with \displaystyle \frac{3}{4} of it with pepperonis on top, which of the following equations will show how many pepperonis will you have on your pizza?

Possible Answers:

\displaystyle pepperonis=\frac{4}{8}\cdot \frac{3}{4}

\displaystyle pepperonis=4\cdot8\cdot \frac{3}{4}

\displaystyle pepperonis=\frac{8}{4}\cdot \frac{3}{4}

\displaystyle pepperonis=(8\cdot\frac{3}{4}) + 4

\displaystyle pepperonis=8+4+\frac{3}{4}

Correct answer:

\displaystyle pepperonis=4\cdot8\cdot \frac{3}{4}

Explanation:

It would help to first write out all our number with their units attached:

\displaystyle \frac{4pepperionis}{slice}

\displaystyle \frac{8 slices}{pizza}

\displaystyle \frac{3}{4}pizza

From here, we can use the units to cancel out until we have \displaystyle \frac{pepperonis}{pizza}:

\displaystyle \frac{4pepperonis}{slice}\cdot\frac{8slices}{pizza}\cdot \frac{3pizza}{4pizza}

 

Example Question #2282 : Algebra Ii

Set up the equation:  Twice a number more than sixteen is forty.

Possible Answers:

\displaystyle 2x+16=40

\displaystyle 2(2x+16)=40

\displaystyle 2x+32=40

\displaystyle 2(x+16)=40

\displaystyle 2(x+32)=40

Correct answer:

\displaystyle 2x+16=40

Explanation:

Split the sentence into parts.

Twice a number:  \displaystyle 2x

Twice a number more than sixteen: \displaystyle 2x+16

Is forty:  \displaystyle =40

Combine the parts to form the equation.

The answer is:  \displaystyle 2x+16=40

Example Question #91 : Equations

Set up the equation:  Five less than three times a number is eight.

Possible Answers:

\displaystyle 3(x-5) =8

\displaystyle 5-3x=8

\displaystyle 3x-5 =8

\displaystyle 3(5-x)=8

\displaystyle -5 -3x=8

Correct answer:

\displaystyle 3x-5 =8

Explanation:

Break up the sentence into parts.

Three times a number:  \displaystyle 3x

Five less than three times a number:  \displaystyle 3x-5

Is eight:  \displaystyle =8

Combine the parts to form the equation.

The answer is:  \displaystyle 3x-5 =8

Example Question #2284 : Algebra Ii

Set up the equation:  Six less than three times the square root of a number is four.

Possible Answers:

\displaystyle 3\sqrt{x-6}=4

\displaystyle 6-\sqrt{3x}=4

\displaystyle 6-3\sqrt{x}=4

\displaystyle \sqrt{3x}-6=4

\displaystyle 3\sqrt{x}-6=4

Correct answer:

\displaystyle 3\sqrt{x}-6=4

Explanation:

Break up the sentence into parts.

The square root of a number:  \displaystyle \sqrt{x}

Three times the square root of a number:  \displaystyle 3\sqrt{x}

Six less than three times the square root of a number:  \displaystyle 3\sqrt{x}-6

Is four:  \displaystyle =4

Combine the parts to form the equation.

The answer is:  \displaystyle 3\sqrt{x}-6=4

Example Question #2285 : Algebra Ii

Set up the equation:  Four less than than twice the square root of a number is nine.

Possible Answers:

\displaystyle \sqrt{2x-4}=9

\displaystyle 4-2\sqrt{x}=9

\displaystyle \sqrt{2x}-4=9

\displaystyle 4-\sqrt{2x}=9

\displaystyle 2\sqrt{x}-4=9

Correct answer:

\displaystyle 2\sqrt{x}-4=9

Explanation:

The square root of a number:  \displaystyle \sqrt{x}

Twice the square root of a number:  \displaystyle 2\sqrt{x}

Four less than than twice the square root of a number:  \displaystyle 2\sqrt{x}-4

Is nine:  \displaystyle =9

Combine the parts to form the equation.

The answer is:  \displaystyle 2\sqrt{x}-4=9

Example Question #2281 : Algebra Ii

Set up the equation:  Four times the fourth root of twice a number is four.

Possible Answers:

\displaystyle 8\sqrt[4]{2x} =4

\displaystyle \sqrt[4]{8x} =4

\displaystyle 8\sqrt[4]{x} =4

\displaystyle 4\sqrt[4]{8x} =4

\displaystyle 4\sqrt[4]{2x} =4

Correct answer:

\displaystyle 4\sqrt[4]{2x} =4

Explanation:

Break up the sentence into parts.

Twice a number:  \displaystyle 2x

The fourth root of twice a number:  \displaystyle \sqrt[4]{2x}

Four times the fourth root of twice a number: \displaystyle 4\sqrt[4]{2x}

Is four:  \displaystyle =4

The answer is: \displaystyle 4\sqrt[4]{2x} =4

Example Question #91 : Setting Up Equations

Set up the equation:  The sum of the square root of a number and the cube root of twice the number is seven.

Possible Answers:

\displaystyle \sqrt{x}+2\sqrt[3]{x} =7

\displaystyle \sqrt{x}+\sqrt[3]{2x} =7

\displaystyle \sqrt[3]{3x} =7

\displaystyle \sqrt[3]{\sqrt{x}+2x} =7

\displaystyle (\sqrt{3x} )^3 =7

Correct answer:

\displaystyle \sqrt{x}+\sqrt[3]{2x} =7

Explanation:

Break up the sentence into parts.

The square root of a number:  \displaystyle \sqrt{x}

The cube root of twice the number:  \displaystyle \sqrt[3]{2x}

The sum of the square root of a number and the cube root of twice the number:

\displaystyle \sqrt{x}+\sqrt[3]{2x}

Is seven:  \displaystyle =7

The answer is:  \displaystyle \sqrt{x}+\sqrt[3]{2x} =7

Example Question #2288 : Algebra Ii

Set up the equation:  Two less than a fifth of a number squared is eighteen.

Possible Answers:

\displaystyle \frac{1}{5}x^2-2=18

\displaystyle \frac{1}{5}(x^2-2)=18

\displaystyle 5x^2-2=18

\displaystyle (\frac{1}{5}x)^2-2=18

\displaystyle \frac{1}{5}(2-x^2)=18

Correct answer:

\displaystyle \frac{1}{5}x^2-2=18

Explanation:

Break up the sentence into parts.

A fifth of a number squared:  \displaystyle \frac{1}{5}x^2

Two less than a fifth of a number squared:  \displaystyle \frac{1}{5}x^2-2

Is eighteen:  \displaystyle =18

Combine the parts to form the equation.

The answer is:  \displaystyle \frac{1}{5}x^2-2=18

Example Question #91 : Equations

Set up the equation:  Seven less than the fourth root of three times a number is nine.

Possible Answers:

\displaystyle 7-\sqrt[4]{3x} = 9

\displaystyle \sqrt[4]{3x}-7 = 9

\displaystyle \sqrt[4]{7-3x} = 9

\displaystyle 3\sqrt[4]{x}-7 = 9

\displaystyle \sqrt[4]{3x-7 }= 9

Correct answer:

\displaystyle \sqrt[4]{3x}-7 = 9

Explanation:

Break up the sentence into parts.

Three times a number:  \displaystyle 3x

Fourth root of three times a number:  \displaystyle \sqrt[4]{3x}

Seven less than the fourth root of three times a number:  \displaystyle \sqrt[4]{3x}-7

Is nine:  \displaystyle =9

Combine the parts to form the equation.

The answer is:  \displaystyle \sqrt[4]{3x}-7 = 9

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