Algebra, NAPX-H4-NC32 SA

Question

{{{question}}}

Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

721

Question

Joe is 34\dfrac{3}{4} the age of Nick.

Kevin is 23\dfrac{2}{3} the age of Nick.

Joe is 3 years older than Kevin.

How old is Nick in years?

Worked Solution
JJ = 34N ... (1)\dfrac{3}{4} N \ ... \ (1)
KK = 23N ... (2)\dfrac{2}{3} N \ ... \ (2)

Since Joe is 3 years older than Kevin:
J − KJ \ - \ K = 3
34N − 23N\dfrac{3}{4} N \ - \ \dfrac{2}{3} N = 3
N(912 − 812)N \bigg( \dfrac{9}{12} \ - \ \dfrac{8}{12} \bigg) = 3
N×112N \times \dfrac{1}{12} = 3
NN = 36

∴\therefore Nick is 36 years old

Question Type

Answer Box

Variables

Variable nameVariable value
question
Joe is $\dfrac{3}{4}$ the age of Nick. Kevin is $\dfrac{2}{3}$ the age of Nick. Joe is 3 years older than Kevin. How old is Nick in years?
workedSolution
| | | | ------------- | ---------- | | $J$ | \= $\dfrac{3}{4} N \ ... \ (1)$ | | $K$ | \= $\dfrac{2}{3} N \ ... \ (2)$ |

Since Joe is 3 years older than Kevin:
| | | | ------------: | ---------- | | $J \ - \ K$ | \= 3 | | $\dfrac{3}{4} N \ - \ \dfrac{2}{3} N$ | \= 3 | | $N \bigg( \dfrac{9}{12} \ - \ \dfrac{8}{12} \bigg)$ | \= 3 | | $N \times \dfrac{1}{12}$ | \= 3 | | $N$ | \= {{{correctAnswer0}}} |

$\therefore$ Nick is {{{correctAnswer0}}} years old
correctAnswer0
36
prefix0
suffix0
years

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
correctAnswer036

years

Variant 1

DifficultyLevel

724

Question

Mork is 25\dfrac{2}{5} the age of Conrad.

Orson is 13\dfrac{1}{3} the age of Conrad.

Mork is 5 years older than Orson.

How old is Conrad in years?

Worked Solution
MM = 25C ... (1)\dfrac{2}{5} C \ ... \ (1)
OO = 13C ... (2)\dfrac{1}{3} C \ ... \ (2)

Since Mork is 5 years older than Orson:
M − OM \ - \ O = 5
25C − 13C\dfrac{2}{5} C \ - \ \dfrac{1}{3} C = 5
C(615 − 515)C \bigg( \dfrac{6}{15} \ - \ \dfrac{5}{15} \bigg) = 5
C×115C \times \dfrac{1}{15} = 5
NN = 75

∴\therefore Conrad is 75 years old

Question Type

Answer Box

Variables

Variable nameVariable value
question
Mork is $\dfrac{2}{5}$ the age of Conrad. Orson is $\dfrac{1}{3}$ the age of Conrad. Mork is 5 years older than Orson. How old is Conrad in years?
workedSolution
| | | | ------------- | ---------- | | $M$ | \= $\dfrac{2}{5} C \ ... \ (1)$ | | $O$ | \= $\dfrac{1}{3} C \ ... \ (2)$ |

Since Mork is 5 years older than Orson:
| | | | ------------: | ---------- | | $M \ - \ O$ | \= 5 | | $\dfrac{2}{5} C \ - \ \dfrac{1}{3} C$ | \= 5 | | $C \bigg( \dfrac{6}{15} \ - \ \dfrac{5}{15} \bigg)$ | \= 5 | | $C \times \dfrac{1}{15}$ | \= 5 | | $N$ | \= {{{correctAnswer0}}} |

$\therefore$ Conrad is {{{correctAnswer0}}} years old
correctAnswer0
75
prefix0
suffix0
years

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
correctAnswer075

years

Variant 2

DifficultyLevel

720

Question

Han is 12\dfrac{1}{2} the age of Darth.

Luke is 13\dfrac{1}{3} the age of Darth.

Han is 6 years older than Luke.

How old is Darth in years?

Worked Solution
HH = 12D ... (1)\dfrac{1}{2} D \ ... \ (1)
LL = 13D ... (2)\dfrac{1}{3} D \ ... \ (2)

Since Han is 6 years older than Luke:
H − LH \ - \ L = 6
12D − 13D\dfrac{1}{2} D \ - \ \dfrac{1}{3} D = 6
D(36 − 26)D \bigg( \dfrac{3}{6} \ - \ \dfrac{2}{6} \bigg) = 6
D×16D \times \dfrac{1}{6} = 6
DD = 36

∴\therefore Darth is 36 years old

Question Type

Answer Box

Variables

Variable nameVariable value
question
Han is $\dfrac{1}{2}$ the age of Darth. Luke is $\dfrac{1}{3}$ the age of Darth. Han is 6 years older than Luke. How old is Darth in years?
workedSolution
| | | | ------------- | ---------- | | $H$ | \= $\dfrac{1}{2} D \ ... \ (1)$ | | $L$ | \= $\dfrac{1}{3} D \ ... \ (2)$ |

Since Han is 6 years older than Luke:
| | | | ------------: | ---------- | | $H \ - \ L$ | \= 6 | | $\dfrac{1}{2} D \ - \ \dfrac{1}{3} D$ | \= 6 | | $D \bigg( \dfrac{3}{6} \ - \ \dfrac{2}{6} \bigg)$ | \= 6 | | $D \times \dfrac{1}{6}$ | \= 6 | | $D$ | \= {{{correctAnswer0}}} |

$\therefore$ Darth is {{{correctAnswer0}}} years old
correctAnswer0
36
prefix0
suffix0
years

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
correctAnswer036

years

Variant 3

DifficultyLevel

728

Question

Max is 47\dfrac{4}{7} the age of Chief.

Barbara is 58\dfrac{5}{8} the age of Chief.

Barbara is 3 years older than Max.

How old is Chief in years?

Worked Solution
MM = 47C ... (1)\dfrac{4}{7} C \ ... \ (1)
BB = 58C ... (2)\dfrac{5}{8} C \ ... \ (2)

Since Barbara is 3 years older than Max:
B − MB \ - \ M = 3
58C − 47C\dfrac{5}{8} C \ - \ \dfrac{4}{7} C = 3
C(3556 − 3256)C \bigg( \dfrac{35}{56} \ - \ \dfrac{32}{56} \bigg) = 3
C×356C \times \dfrac{3}{56} = 3
3C3C = 168
CC = 56

∴\therefore Chief is 56 years old

Question Type

Answer Box

Variables

Variable nameVariable value
question
Max is $\dfrac{4}{7}$ the age of Chief. Barbara is $\dfrac{5}{8}$ the age of Chief. Barbara is 3 years older than Max. How old is Chief in years?
workedSolution
| | | | ------------- | ---------- | | $M$ | \= $\dfrac{4}{7} C \ ... \ (1)$ | | $B$ | \= $\dfrac{5}{8} C \ ... \ (2)$ |

Since Barbara is 3 years older than Max:
| | | | ------------: | ---------- | | $B \ - \ M$ | \= 3| | $\dfrac{5}{8} C \ - \ \dfrac{4}{7} C$ | \= 3 | | $C \bigg( \dfrac{35}{56} \ - \ \dfrac{32}{56} \bigg)$ | \= 3 | | $C \times \dfrac{3}{56}$ | \= 3 | |$3C$ | \= 168 | |$C$ | \= {{{correctAnswer0}}} |

$\therefore$ Chief is {{{correctAnswer0}}} years old
correctAnswer0
56
prefix0
suffix0
years

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
correctAnswer056

years

Variant 4

DifficultyLevel

724

Question

Minn is 49\dfrac{4}{9} the age of Jae.

Ari is 512\dfrac{5}{12} the age of Jae.

Minn is 2 years older than Ari.

How old is Jae in years?

Worked Solution
MM = 49J ... (1)\dfrac{4}{9} J \ ... \ (1)
AA = 512J ... (2)\dfrac{5}{12} J \ ... \ (2)

Since Minn is 2 years older than Ari:
M − AM \ - \ A = 2
49J − 512J\dfrac{4}{9} J \ - \ \dfrac{5}{12} J = 2
J(1636 − 1536)J \bigg( \dfrac{16}{36} \ - \ \dfrac{15}{36} \bigg) = 2
J×136J \times \dfrac{1}{36} = 2
JJ = 72

∴\therefore Jae is 72 years old

Question Type

Answer Box

Variables

Variable nameVariable value
question
Minn is $\dfrac{4}{9}$ the age of Jae. Ari is $\dfrac{5}{12}$ the age of Jae. Minn is 2 years older than Ari. How old is Jae in years?
workedSolution
| | | | ------------- | ---------- | | $M$ | \= $\dfrac{4}{9} J \ ... \ (1)$ | | $A$ | \= $\dfrac{5}{12} J \ ... \ (2)$ |

Since Minn is 2 years older than Ari:
| | | | ------------: | ---------- | | $M \ - \ A$ | \= 2 | | $\dfrac{4}{9} J \ - \ \dfrac{5}{12} J$ | \= 2 | | $J \bigg( \dfrac{16}{36} \ - \ \dfrac{15}{36} \bigg)$ | \= 2 | | $J \times \dfrac{1}{36}$ | \= 2 | | $J$ | \= {{{correctAnswer0}}} |

$\therefore$ Jae is {{{correctAnswer0}}} years old
correctAnswer0
72
prefix0
suffix0
years

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
correctAnswer072

years

Variant 5

DifficultyLevel

721

Question

Fatima is 35\dfrac{3}{5} the age of Ahmed.

Dina is 12\dfrac{1}{2} the age of Ahmed.

Fatima is 5 years older than Dina.

How old is Ahmed in years?

Worked Solution
FF = 35A ... (1)\dfrac{3}{5} A \ ... \ (1)
DD = 12A ... (2)\dfrac{1}{2} A \ ... \ (2)

Since Fatima is 5 years older than Dina:
F − DF \ - \ D = 5
35A − 12A\dfrac{3}{5} A \ - \ \dfrac{1}{2} A = 5
A(610 − 510)A \bigg( \dfrac{6}{10} \ - \ \dfrac{5}{10} \bigg) = 5
A×110A \times \dfrac{1}{10} = 5
AA = 50

∴\therefore Ahmed is 50 years old

Question Type

Answer Box

Variables

Variable nameVariable value
question
Fatima is $\dfrac{3}{5}$ the age of Ahmed. Dina is $\dfrac{1}{2}$ the age of Ahmed. Fatima is 5 years older than Dina. How old is Ahmed in years?
workedSolution
| | | | ------------- | ---------- | | $F$ | \= $\dfrac{3}{5} A \ ... \ (1)$ | | $D$ | \= $\dfrac{1}{2} A \ ... \ (2)$ |

Since Fatima is 5 years older than Dina:
| | | | ------------: | ---------- | | $F \ - \ D$ | \= 5 | | $\dfrac{3}{5} A \ - \ \dfrac{1}{2} A$ | \= 5 | | $A \bigg( \dfrac{6}{10} \ - \ \dfrac{5}{10} \bigg)$ | \= 5 | | $A \times \dfrac{1}{10}$ | \= 5 | | $A$ | \= {{{correctAnswer0}}} |

$\therefore$ Ahmed is {{{correctAnswer0}}} years old
correctAnswer0
50
prefix0
suffix0
years

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

years

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