Algebra, NAPX-G4-NC30 SA

Question

{{{question}}}

Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

708

Question

Sue and Belinda have total combined savings of $32.

If 15\dfrac{1}{5} of Sue's savings equals 13\dfrac{1}{3} of Belinda's savings, how much has Belinda saved?

Worked Solution
15S\dfrac{1}{5} S = 13B\dfrac{1}{3} B
SS = 53B ... (1)\dfrac{5}{3} B \ ... \ (1)
S+BS + B = 32 ... (2)

Substitute (1) into (2)
53B+B\dfrac{5}{3} B + B = 32
83B\dfrac{8}{3} B = 32
BB = 32 ×38\times \dfrac{3}{8}
= $12

Question Type

Answer Box

Variables

Variable nameVariable value
question
Sue and Belinda have total combined savings of $32. If $\dfrac{1}{5}$ of Sue's savings equals $\dfrac{1}{3}$ of Belinda's savings, how much has Belinda saved?
workedSolution
| | | | ------------: | ---------- | | $\dfrac{1}{5} S$ | \= $\dfrac{1}{3} B$ | | $S$ | \= $\dfrac{5}{3} B \ ... \ (1)$ | | $S + B$ | \= 32 ... (2) |

Substitute (1) into (2)
| | | | ------------: | ---------- | | $\dfrac{5}{3} B + B$ | \= 32 | | $\dfrac{8}{3} B$ | \= 32 | | $B$| \= 32 $\times \dfrac{3}{8}$| | | \= {{{prefix0}}}{{{correctAnswer0}}} |
correctAnswer0
12
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
correctAnswer012

$

Variant 1

DifficultyLevel

719

Question

Blake and Ryan have total combined savings of $5400.

If 16\dfrac{1}{6} of Blake's savings equals 14\dfrac{1}{4} of Ryan's savings, how much has Ryan saved?

Worked Solution
16B\dfrac{1}{6} B = 14R\dfrac{1}{4} R
BB = 64R\dfrac{6}{4} R
BB = 32R ... (1)\dfrac{3}{2} R \ ... \ (1)
B+RB + R = 5400 ... (2)

Substitute (1) into (2)
32R+R\dfrac{3}{2} R + R = 5400
52R\dfrac{5}{2} R = 5400
RR = 5400 ×25\times \dfrac{2}{5}
= $2160

Question Type

Answer Box

Variables

Variable nameVariable value
question
Blake and Ryan have total combined savings of $5400. If $\dfrac{1}{6}$ of Blake's savings equals $\dfrac{1}{4}$ of Ryan's savings, how much has Ryan saved?
workedSolution
| | | | ------------: | ---------- | | $\dfrac{1}{6} B$ | \= $\dfrac{1}{4} R$ | | $B$ | \= $\dfrac{6}{4} R$ | | $B$ | \= $\dfrac{3}{2} R \ ... \ (1)$ | | $B + R$ | \= 5400 ... (2) |

Substitute (1) into (2)
| | | | ------------: | ---------- | | $\dfrac{3}{2} R + R$ | \= 5400 | | $\dfrac{5}{2} R$ | \= 5400 | | $R$| \= 5400 $\times \dfrac{2}{5}$| | | \= {{{prefix0}}}{{{correctAnswer0}}} |
correctAnswer0
2160
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
correctAnswer02160

$

Variant 2

DifficultyLevel

722

Question

Ellen and Jocelyn have total combined savings of $123 500.

If 23\dfrac{2}{3} of Ellen's savings equals 35\dfrac{3}{5} of Jocelyn's savings, how much has Jocelyn saved?

Worked Solution
23E\dfrac{2}{3} E = 35J\dfrac{3}{5} J
EE = 910J ... (1)\dfrac{9}{10} J \ ... \ (1)
E+JE + J = 123 500 ... (2)

Substitute (1) into (2)
910J+J\dfrac{9}{10} J + J = 123 500
1910J\dfrac{19}{10} J = 123 500
JJ = 123 500 ×1019\times \dfrac{10}{19}
= 65 000

Question Type

Answer Box

Variables

Variable nameVariable value
question
Ellen and Jocelyn have total combined savings of $123 500. If $\dfrac{2}{3}$ of Ellen's savings equals $\dfrac{3}{5}$ of Jocelyn's savings, how much has Jocelyn saved?
workedSolution
| | | | ------------: | ---------- | | $\dfrac{2}{3} E$ | \= $\dfrac{3}{5} J$ | | $E$ | \= $\dfrac{9}{10} J \ ... \ (1)$ | | $E + J$ | \= 123 500 ... (2) |

Substitute (1) into (2)
| | | | ------------: | ---------- | | $\dfrac{9}{10} J + J$ | \= 123 500 | | $\dfrac{19}{10} J$ | \= 123 500 | | $J$| \= 123 500 $\times \dfrac{10}{19}$| | | \= 65 000 |
correctAnswer0
65000
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
correctAnswer065000

$

Variant 3

DifficultyLevel

717

Question

Will and Ben have total combined savings of $12 810.

If 45\dfrac{4}{5} of Will's savings equals 14\dfrac{1}{4} of Ben's savings, how much has Ben saved?

Worked Solution
45W\dfrac{4}{5} W = 14B\dfrac{1}{4} B
WW = 516B ... (1)\dfrac{5}{16} B \ ... \ (1)
W+BW + B = 12 810 ... (2)

Substitute (1) into (2)
516B+B\dfrac{5}{16} B + B = 12 810
2116B\dfrac{21}{16} B = 12 810
BB = 12 810 ×1621\times \dfrac{16}{21}
= $9760

Question Type

Answer Box

Variables

Variable nameVariable value
question
Will and Ben have total combined savings of $12 810. If $\dfrac{4}{5}$ of Will's savings equals $\dfrac{1}{4}$ of Ben's savings, how much has Ben saved?
workedSolution
| | | | ------------: | ---------- | | $\dfrac{4}{5} W$ | \= $\dfrac{1}{4} B$ | | $W$ | \= $\dfrac{5}{16} B \ ... \ (1)$ | | $W + B$ | \= 12 810 ... (2) |

Substitute (1) into (2)
| | | | ------------: | ---------- | | $\dfrac{5}{16} B + B$ | \= 12 810 | | $\dfrac{21}{16} B$ | \= 12 810 | | $B$| \= 12 810 $\times \dfrac{16}{21}$| | | \= {{{prefix0}}}{{{correctAnswer0}}} |
correctAnswer0
9760
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
correctAnswer09760

$

Variant 4

DifficultyLevel

724

Question

Batman and Robin have total combined savings of $1 776 000.

If 13\dfrac{1}{3} of Batman's savings equals 910\dfrac{9}{10} of Robin's savings, how much has Robin saved?

Worked Solution
13B\dfrac{1}{3} B = 910R\dfrac{9}{10} R
BB = 2710R ... (1)\dfrac{27}{10} R \ ... \ (1)
B+RB + R = 1 776 000 ... (2)

Substitute (1) into (2)
2710R+R\dfrac{27}{10} R + R = 1 776 000
3710R\dfrac{37}{10} R = 1 776 000
RR = 1 776 000 ×1037\times \dfrac{10}{37}
= 480 000

Question Type

Answer Box

Variables

Variable nameVariable value
question
Batman and Robin have total combined savings of $1 776 000. If $\dfrac{1}{3}$ of Batman's savings equals $\dfrac{9}{10}$ of Robin's savings, how much has Robin saved?
workedSolution
| | | | ------------: | ---------- | | $\dfrac{1}{3} B$ | \= $\dfrac{9}{10} R$ | | $B$ | \= $\dfrac{27}{10} R \ ... \ (1)$ | | $B + R$ | \= 1 776 000 ... (2) |

Substitute (1) into (2)
| | | | ------------: | ---------- | | $\dfrac{27}{10} R + R$ | \= 1 776 000 | | $\dfrac{37}{10} R$ | \= 1 776 000 | | $R$| \= 1 776 000 $\times \dfrac{10}{37}$| | | \= 480 000 |
correctAnswer0
480000
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
correctAnswer0480000

$

Variant 5

DifficultyLevel

709

Question

Anna and Kristoff have total combined savings of $45.

If 15\dfrac{1}{5} of Anna's savings equals 45\dfrac{4}{5} of Kristoff's savings, how much has Kristoff saved?

Worked Solution
15A\dfrac{1}{5} A = 45K\dfrac{4}{5} K
AA = 4K ... (1)
A+KA + K = 45 ... (2)

Substitute (1) into (2)
4K+K4K + K = 45
5K5 K = 45
KK = $9

Question Type

Answer Box

Variables

Variable nameVariable value
question
Anna and Kristoff have total combined savings of $45. If $\dfrac{1}{5}$ of Anna's savings equals $\dfrac{4}{5}$ of Kristoff's savings, how much has Kristoff saved?
workedSolution
| | | | ------------: | ---------- | | $\dfrac{1}{5} A$ | \= $\dfrac{4}{5} K$ | | $A$ | \= 4K ... (1) | | $A + K$ | \= 45 ... (2) |

Substitute (1) into (2)
| | | | ------------: | ---------- | | $4K + K$ | \= 45 | | $5 K$ | \= 45 | | $K$| = {{{prefix0}}}{{{correctAnswer0}}} |
correctAnswer0
9
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
correctAnswer09

$

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