Algebra, NAPX-G4-CA29 SA

Question

{{{question}}}

Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

729

Question

250=255+1x\dfrac{2}{50} = \dfrac{2}{55} + \dfrac{1}{\large x}

Find the value of x\large x?

Worked Solution
1x\dfrac{1}{\large x} = 250−255\dfrac{2}{50} - \dfrac{2}{55}
= 1102750 − 1002750\dfrac{110}{2750}\ -\ \dfrac{100}{2750}
= 102750\dfrac{10}{2750}
= 1275\dfrac{1}{275}
∴ x\therefore \ \large x = 275

Question Type

Answer Box

Variables

Variable nameVariable value
question
$\dfrac{2}{50} = \dfrac{2}{55} + \dfrac{1}{\large x}$ Find the value of $\large x$?
workedSolution
| | | | -------------: | ---------- | | $\dfrac{1}{\large x}$ | \= $\dfrac{2}{50} - \dfrac{2}{55}$ | | | \= $\dfrac{110}{2750}\ -\ \dfrac{100}{2750}$ | | | \= $\dfrac{10}{2750}$ | | | \= $\dfrac{1}{275}$ | | $\therefore \ \large x$ | \= {{{correctAnswer0}}} |
correctAnswer0
275
prefix0
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer0275

Variant 1

DifficultyLevel

723

Question

220=225+1x\dfrac{2}{20} = \dfrac{2}{25} + \dfrac{1}{\large x}

Find the value of x\large x?

Worked Solution
1x\dfrac{1}{\large x} = 220−225\dfrac{2}{20} - \dfrac{2}{25}
= 50500 − 40500\dfrac{50}{500}\ -\ \dfrac{40}{500}
= 10500\dfrac{10}{500}
= 150\dfrac{1}{50}
∴ x\therefore \ \large x = 50

Question Type

Answer Box

Variables

Variable nameVariable value
question
$\dfrac{2}{20} = \dfrac{2}{25} + \dfrac{1}{\large x}$ Find the value of $\large x$?
workedSolution
| | | | -------------: | ---------- | | $\dfrac{1}{\large x}$ | \= $\dfrac{2}{20} - \dfrac{2}{25}$ | | | \= $\dfrac{50}{500}\ -\ \dfrac{40}{500}$ | | | \= $\dfrac{10}{500}$ | | | \= $\dfrac{1}{50}$ | | $\therefore \ \large x$ | \= {{{correctAnswer0}}} |
correctAnswer0
50
prefix0
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer050

Variant 2

DifficultyLevel

725

Question

210=215+1x\dfrac{2}{10} = \dfrac{2}{15} + \dfrac{1}{\large x}

Find the value of x\large x?

Worked Solution
1x\dfrac{1}{\large x} = 210−215\dfrac{2}{10} - \dfrac{2}{15}
= 30150 − 20150\dfrac{30}{150}\ -\ \dfrac{20}{150}
= 10150\dfrac{10}{150}
= 115\dfrac{1}{15}
∴ x\therefore \ \large x = 15

Question Type

Answer Box

Variables

Variable nameVariable value
question
$\dfrac{2}{10} = \dfrac{2}{15} + \dfrac{1}{\large x}$ Find the value of $\large x$?
workedSolution
| | | | -------------: | ---------- | | $\dfrac{1}{\large x}$ | \= $\dfrac{2}{10} - \dfrac{2}{15}$ | | | \= $\dfrac{30}{150}\ -\ \dfrac{20}{150}$ | | | \= $\dfrac{10}{150}$ | | | \= $\dfrac{1}{15}$ | | $\therefore \ \large x$ | \= {{{correctAnswer0}}} |
correctAnswer0
15
prefix0
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer015

Variant 3

DifficultyLevel

729

Question

230=235+1x\dfrac{2}{30} = \dfrac{2}{35} + \dfrac{1}{\large x}

Find the value of x\large x?

Worked Solution
1x\dfrac{1}{\large x} = 230−235\dfrac{2}{30} - \dfrac{2}{35}
= 701050 − 601050\dfrac{70}{1050}\ -\ \dfrac{60}{1050}
= 101050\dfrac{10}{1050}
= 1105\dfrac{1}{105}
∴ x\therefore \ \large x = 105

Question Type

Answer Box

Variables

Variable nameVariable value
question
$\dfrac{2}{30} = \dfrac{2}{35} + \dfrac{1}{\large x}$ Find the value of $\large x$?
workedSolution
| | | | -------------: | ---------- | | $\dfrac{1}{\large x}$ | \= $\dfrac{2}{30} - \dfrac{2}{35}$ | | | \= $\dfrac{70}{1050}\ -\ \dfrac{60}{1050}$ | | | \= $\dfrac{10}{1050}$ | | | \= $\dfrac{1}{105}$ | | $\therefore \ \large x$ | \= {{{correctAnswer0}}} |
correctAnswer0
105
prefix0
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer0105

Variant 4

DifficultyLevel

729

Question

240=245+1x\dfrac{2}{40} = \dfrac{2}{45} + \dfrac{1}{\large x}

Find the value of x\large x?

Worked Solution
1x\dfrac{1}{\large x} = 240−245\dfrac{2}{40} - \dfrac{2}{45}
= 901800 − 801800\dfrac{90}{1800}\ -\ \dfrac{80}{1800}
= 101800\dfrac{10}{1800}
= 1180\dfrac{1}{180}
∴ x\therefore \ \large x = 180

Question Type

Answer Box

Variables

Variable nameVariable value
question
$\dfrac{2}{40} = \dfrac{2}{45} + \dfrac{1}{\large x}$ Find the value of $\large x$?
workedSolution
| | | | -------------: | ---------- | | $\dfrac{1}{\large x}$ | \= $\dfrac{2}{40} - \dfrac{2}{45}$ | | | \= $\dfrac{90}{1800}\ -\ \dfrac{80}{1800}$ | | | \= $\dfrac{10}{1800}$ | | | \= $\dfrac{1}{180}$ | | $\therefore \ \large x$ | \= {{{correctAnswer0}}} |
correctAnswer0
180
prefix0
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer0180

Variant 5

DifficultyLevel

732

Question

260=265+1x\dfrac{2}{60} = \dfrac{2}{65} + \dfrac{1}{\large x}

Find the value of x\large x?

Worked Solution
1x\dfrac{1}{\large x} = 260−265\dfrac{2}{60} - \dfrac{2}{65}
= 1303900 − 1203900\dfrac{130}{3900}\ -\ \dfrac{120}{3900}
= 103900\dfrac{10}{3900}
= 1390\dfrac{1}{390}
∴ x\therefore \ \large x = 390

Question Type

Answer Box

Variables

Variable nameVariable value
question
$\dfrac{2}{60} = \dfrac{2}{65} + \dfrac{1}{\large x}$ Find the value of $\large x$?
workedSolution
| | | | -------------: | ---------- | | $\dfrac{1}{\large x}$ | \= $\dfrac{2}{60} - \dfrac{2}{65}$ | | | \= $\dfrac{130}{3900}\ -\ \dfrac{120}{3900}$ | | | \= $\dfrac{10}{3900}$ | | | \= $\dfrac{1}{390}$ | | $\therefore \ \large x$ | \= {{{correctAnswer0}}} |
correctAnswer0
390
prefix0
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer0390

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