Number, NAPX-H4-NC16, NAPX-H3-NC22

Question

{{{question}}}

Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

617

Question

Enya made a mobile phone call that lasted 41 minutes.

Her mobile phone provider charges her 31 cents per minute for calls.

Enya estimated that the total cost of the phone call was about $12.

Enya's estimate was

Worked Solution

An estimate of the cost could be just over:

40 minutes × 30 cents = $12

∴ $12 estimate is less than the actual cost.

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
Enya made a mobile phone call that lasted 41 minutes. Her mobile phone provider charges her 31 cents per minute for calls. Enya estimated that the total cost of the phone call was about $12. Enya's estimate was
workedSolution
An estimate of the cost could be just over: 40 minutes × 30 cents = $12 ∴ $12 estimate is {{{correctAnswer}}}
correctAnswer
less than the actual cost.

Answers

Is Correct?Answer
x

more than the actual cost.

x

equal to the actual cost.

✓

less than the actual cost.

Variant 1

DifficultyLevel

618

Question

A farmer plants 29 rows of corn with 41 seeds per row.

He estimates the total number of seeds is about 1200.

His estimate was:

Worked Solution
Estimate: 30 ×\times 40 = 1200

Actual: 29 ×\times 41 = (30 −- 1) ×\times (40 + 1)
= 30 ×\times 40 + 30 ×\times 1 −- 1 ×\times 40 −- 1 ×\times 1
= 1200 + 30 −- 40 −- 1
= 1189

∴\therefore The estimate of 1200 is more than the actual number of seeds..

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A farmer plants 29 rows of corn with 41 seeds per row. He estimates the total number of seeds is about 1200. His estimate was:
workedSolution
| | | - | | Estimate: 30 $\times$ 40 = 1200 |

| | | | ----------------------------------:| --------------------------------------------------------------------- | | Actual: 29 $\times$ 41 | = (30 $-$ 1) $\times$ (40 + 1) | | | = 30 $\times$ 40 + 30 $\times$ 1 $-$ 1 $\times$ 40 $-$ 1 $\times$ 1 | | | = 1200 + 30 $-$ 40 $-$ 1 | | | = 1189 |

$\therefore$ The estimate of 1200 is {{{correctAnswer}}}.
correctAnswer
more than the actual number of seeds.

Answers

Is Correct?Answer
✓

more than the actual number of seeds.

x

equal to the actual number of seeds.

x

less than the actual number of seeds.

Variant 2

DifficultyLevel

619

Question

A swimmer trains 52 weeks a year and swims 18 km per week.

She estimates the total distance she swims in a year is about 1000 km.

Her estimate was:

Worked Solution
Estimate: 50 ×\times 20 = 1000

Actual: 52 ×\times 18 = (50 + 2) ×\times (20 −- 2)
= 50 ×\times 20 −- 50 ×\times 2 + 2 ×\times 20 −- 2 ×\times 2
= 1000 −- 100 + 40 −- 4
= 936

∴\therefore The estimate of 1000 is more than the actual number of weeks a year..

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A swimmer trains 52 weeks a year and swims 18 km per week. She estimates the total distance she swims in a year is about 1000 km. Her estimate was:
workedSolution
| | | - | | Estimate: 50 $\times$ 20 = 1000 |

| | | | ----------------------------------:| --------------------------------------------------------------------- | | Actual: 52 $\times$ 18 | = (50 + 2) $\times$ (20 $-$ 2) | | | = 50 $\times$ 20 $-$ 50 $\times$ 2 + 2 $\times$ 20 $-$ 2 $\times$ 2 | | | = 1000 $-$ 100 + 40 $-$ 4 | | | = 936 |

$\therefore$ The estimate of 1000 is {{{correctAnswer}}}.
correctAnswer
more than the actual number of weeks a year.

Answers

Is Correct?Answer
x

less than the actual number of weeks a year.

x

equal to the actual number of weeks a year.

✓

more than the actual number of weeks a year.

Variant 3

DifficultyLevel

620

Question

A baker uses 42 grams of butter per cake and makes 48 cakes.

He estimates the total amount of butter used is about 2000 grams.

His estimate was:

Worked Solution
Estimate: 40 ×\times 50 = 2000

Actual: 42 ×\times 48 = (40 + 2) ×\times (50 −- 2)
= 40 ×\times 50 −- 40 ×\times 2 + 2 ×\times 50 −- 2 ×\times 2
= 2000 −- 80 + 100 −- 4
= 2016

∴\therefore The estimate of 2000 is less than the actual grams of butter..

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A baker uses 42 grams of butter per cake and makes 48 cakes. He estimates the total amount of butter used is about 2000 grams. His estimate was:
workedSolution
| | | - | | Estimate: 40 $\times$ 50 = 2000 |

| | | | ----------------------------------:| --------------------------------------------------------------------- | | Actual: 42 $\times$ 48 | = (40 + 2) $\times$ (50 $-$ 2) | | | = 40 $\times$ 50 $-$ 40 $\times$ 2 + 2 $\times$ 50 $-$ 2 $\times$ 2 | | | = 2000 $-$ 80 + 100 $-$ 4 | | | = 2016 |

$\therefore$ The estimate of 2000 is {{{correctAnswer}}}.
correctAnswer
less than the actual grams of butter.

Answers

Is Correct?Answer
✓

less than the actual grams of butter.

x

more than the actual grams of butter.

x

equal to the actual grams of butter.

Variant 4

DifficultyLevel

621

Question

A printer prints 40 pages per minute and runs for exactly 30 minutes.

A technician estimates the total number of pages printed is about 1200.

His estimate was:

Worked Solution
Estimate: 40 ×\times 30 = 1200

Actual: 40 ×\times 30 = 1200

∴\therefore The estimate of 1200 is equal to the actual number of pages..

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A printer prints 40 pages per minute and runs for exactly 30 minutes. A technician estimates the total number of pages printed is about 1200. His estimate was:
workedSolution
| | | - | | Estimate: 40 $\times$ 30 = 1200 |

| | | | ----------------------------------:| --------------------------------------------------------------------- | | Actual: 40 $\times$ 30 | = 1200 |

$\therefore$ The estimate of 1200 is {{{correctAnswer}}}.
correctAnswer
equal to the actual number of pages.

Answers

Is Correct?Answer
x

more than the actual number of pages.

✓

equal to the actual number of pages.

x

less than the actual number of pages.

Variant 5

DifficultyLevel

622

Question

A cyclist rides 61 km per day for 31 days.

She estimates the total distance she rides is about 1800 km.

Her estimate was:

Worked Solution
Estimate: 60 ×\times 30 = 1800

Actual: 61 ×\times 31 = (60 + 1) ×\times (30 + 1)
= 60 ×\times 30 + 60 ×\times 1 + 1 ×\times 30 + 1 ×\times 1
= 1800 + 60 + 30 + 1
= 1891

∴\therefore The estimate of 1800 is less than the actual distance..

Question Type

Multiple Choice (One Answer)

Variables

Variable nameVariable value
question
A cyclist rides 61 km per day for 31 days. She estimates the total distance she rides is about 1800 km. Her estimate was:
workedSolution
| | | - | | Estimate: 60 $\times$ 30 = 1800 |

| | | | ----------------------------------:| --------------------------------------------------------------------- | | Actual: 61 $\times$ 31 | = (60 + 1) $\times$ (30 + 1) | | | = 60 $\times$ 30 + 60 $\times$ 1 + 1 $\times$ 30 + 1 $\times$ 1 | | | = 1800 + 60 + 30 + 1 | | | = 1891 |

$\therefore$ The estimate of 1800 is {{{correctAnswer}}}.
correctAnswer
less than the actual distance.

Answers

Is Correct?Answer
x

more than the actual distance.

x

equal to the actual distance.

✓

less than the actual distance.

Tags

  • nap_nc
  • staging_suejones