Algebra, NAPX-I4-NC18 SA

Question

{{{question}}}

Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

659

Question

Paul and Simon are saving money so they can visit their grandmother on a holiday.

Paul has $200 and plans to save $50 each week.

Simon has $300 and plans to save $25 each week.

After how many weeks will Paul and Simon have saved the same amount?

Worked Solution

After w\large w weeks,

Paul has saved: 200+50w200+50\large w

Simon has saved: 300+25w300+25\large w

Savings are equal when:
200+50w200+50\large w = 300+25w300+25\large w
25w25\large w = 100
w\large w = 4

∴\therefore Amounts are equal after 4 weeks.

Question Type

Answer Box

Variables

Variable nameVariable value
question
Paul and Simon are saving money so they can visit their grandmother on a holiday. Paul has $200 and plans to save $50 each week. Simon has $300 and plans to save $25 each week. After how many weeks will Paul and Simon have saved the same amount?
workedSolution
After $\large w$ weeks, Paul has saved: $200+50\large w$ Simon has saved: $300+25\large w$ sm_nogap Savings are equal when:
| | | | ------------: | ---------- | | $200+50\large w$ | \= $300+25\large w$ | | $25\large w$ | \= 100 | | $\large w$ | \= {{{correctAnswer0}}} |

$\therefore$ Amounts are equal after {{{correctAnswer0}}} weeks.
correctAnswer0
4
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
correctAnswer04

Variant 1

DifficultyLevel

667

Question

Bracken and Fern are saving money so they can build a granny flat in the backyard.

Bracken has $1500 and plans to save $450 each week.

Fern has $4500 and plans to save $250 each week.

After how many weeks will Bracken and Fern have saved the same amount?

Worked Solution

After w\large w weeks,

Bracken has saved: 1500+450w1500+450\large w

Fern has saved: 4500+250w4500+250\large w

Savings are equal when:
1500+450w1500+450\large w = 4500+250w4500+250\large w
200w200\large w = 3000
w\large w = 15

∴\therefore Amounts are equal after 15 weeks.

Question Type

Answer Box

Variables

Variable nameVariable value
question
Bracken and Fern are saving money so they can build a granny flat in the backyard. Bracken has $1500 and plans to save $450 each week. Fern has $4500 and plans to save $250 each week. After how many weeks will Bracken and Fern have saved the same amount?
workedSolution
After $\large w$ weeks, Bracken has saved: $1500+450\large w$ Fern has saved: $4500+250\large w$ sm_nogap Savings are equal when:
| | | | ------------: | ---------- | | $1500+450\large w$ | \= $4500+250\large w$ | | $200\large w$ | \= 3000 | | $\large w$ | \= {{{correctAnswer0}}} |

$\therefore$ Amounts are equal after {{{correctAnswer0}}} weeks.
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 2

DifficultyLevel

659

Question

Ribena and Oban are saving money so they can stock their greenhouse with plants.

Ribena has $550 and plans to save $25 each week.

Oban has $750 and plans to save $15 each week.

After how many weeks will Ribena and Oban have saved the same amount?

Worked Solution

After w\large w weeks,

Ribena has saved: 550+25w550+25\large w

Oban has saved: 750+15w750+15\large w

Savings are equal when:
550+25w550+25\large w = 750+15w750+15\large w
10w10\large w = 200
w\large w = 20

∴\therefore Amounts are equal after 20 weeks.

Question Type

Answer Box

Variables

Variable nameVariable value
question
Ribena and Oban are saving money so they can stock their greenhouse with plants. Ribena has $550 and plans to save $25 each week. Oban has $750 and plans to save $15 each week. After how many weeks will Ribena and Oban have saved the same amount?
workedSolution
After $\large w$ weeks, Ribena has saved: $550+25\large w$ Oban has saved: $750+15\large w$ sm_nogap Savings are equal when:
| | | | ------------: | ---------- | | $550+25\large w$ | \= $750+15\large w$ | | $10\large w$ | \= 200 | | $\large w$ | \= {{{correctAnswer0}}} |

$\therefore$ Amounts are equal after {{{correctAnswer0}}} weeks.
correctAnswer0
20
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
correctAnswer020

Variant 3

DifficultyLevel

669

Question

Meg and Ryan are saving money for their wedding next year.

Meg has $2600 and plans to save $120 each week.

Ryan has $3800 and plans to save $100 each week.

After how many weeks will Meg and Ryan have saved the same amount?

Worked Solution

After w\large w weeks,

Meg has saved: 2600+120w2600+120\large w

Ryan has saved: 3800+100w3800+100\large w

Savings are equal when:
2600+120w2600+120\large w = 3800+100w3800+100\large w
20w20\large w = 1200
w\large w = 60

∴\therefore Amounts are equal after 60 weeks.

Question Type

Answer Box

Variables

Variable nameVariable value
question
Meg and Ryan are saving money for their wedding next year. Meg has $2600 and plans to save $120 each week. Ryan has $3800 and plans to save $100 each week. After how many weeks will Meg and Ryan have saved the same amount?
workedSolution
After $\large w$ weeks, Meg has saved: $2600+120\large w$ Ryan has saved: $3800+100\large w$ sm_nogap Savings are equal when:
| | | | ------------: | ---------- | | $2600+120\large w$ | \= $3800+100\large w$ | | $20\large w$ | \= 1200 | | $\large w$ | \= {{{correctAnswer0}}} |

$\therefore$ Amounts are equal after {{{correctAnswer0}}} weeks.
correctAnswer0
60
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
correctAnswer060

Variant 4

DifficultyLevel

659

Question

Ketut and Made are saving money so they can stock their new online handmade jewellery store.

Ketut has $540 and plans to save $20 each week.

Made has $660 and plans to save $15 each week.

After how many weeks will Ketut and Made have saved the same amount?

Worked Solution

After w\large w weeks,

Ketut has saved: 540+20w540+20\large w

Made has saved: 660+15w660+15\large w

Savings are equal when:
540+20w540+20\large w = 660+15w660+15\large w
5w5\large w = 120
w\large w = 24

∴\therefore Amounts are equal after 24 weeks.

Question Type

Answer Box

Variables

Variable nameVariable value
question
Ketut and Made are saving money so they can stock their new online handmade jewellery store. Ketut has $540 and plans to save $20 each week. Made has $660 and plans to save $15 each week. After how many weeks will Ketut and Made have saved the same amount?
workedSolution
After $\large w$ weeks, Ketut has saved: $540+20\large w$ Made has saved: $660+15\large w$ sm_nogap Savings are equal when:
| | | | ------------: | ---------- | | $540+20\large w$ | \= $660+15\large w$ | | $5\large w$ | \= 120 | | $\large w$ | \= {{{correctAnswer0}}} |

$\therefore$ Amounts are equal after {{{correctAnswer0}}} weeks.
correctAnswer0
24
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
correctAnswer024

Variant 5

DifficultyLevel

663

Question

Diego and Santiago are saving money so they can buy a fishing boat.

Diego has $4580 and plans to save $55 each week.

Santiago has $5640 and plans to save $45 each week.

After how many weeks will Diego and Santiago have saved the same amount?

Worked Solution

After w\large w weeks,

Diego has saved: 4580+55w4580+55\large w

Santiago has saved: 5640+45w5640+45\large w

Savings are equal when:
4580+55w4580+55\large w = 5640+45w5640+45\large w
10w10\large w = 1060
w\large w = 106

∴\therefore Amounts are equal after 106 weeks.

Question Type

Answer Box

Variables

Variable nameVariable value
question
Diego and Santiago are saving money so they can buy a fishing boat. Diego has $4580 and plans to save $55 each week. Santiago has $5640 and plans to save $45 each week. After how many weeks will Diego and Santiago have saved the same amount?
workedSolution
After $\large w$ weeks, Diego has saved: $4580+55\large w$ Santiago has saved: $5640+45\large w$ sm_nogap Savings are equal when:
| | | | ------------: | ---------- | | $4580+55\large w$ | \= $5640+45\large w$ | | $10\large w$ | \= 1060 | | $\large w$ | \= {{{correctAnswer0}}} |

$\therefore$ Amounts are equal after {{{correctAnswer0}}} weeks.
correctAnswer0
106
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
correctAnswer0106

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