Number_gap-2026_687

Question

{{{question}}}

Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

687

Question

There are 360 animals at a rescue shelter.

Two-thirds of the animals are dogs and the rest are cats. 35% of the dogs are puppies.

How many puppies are at the shelter?

Worked Solution
Number of dogs = 23\dfrac{2}{3} ×\times 360
= 23\dfrac{2}{3} ×\times 3 ×\times 120
= 2 ×\times 120 = 240

Number of puppies = 35% ×\times 240
= 35100\dfrac{35}{100} ×\times 240
= 720\dfrac{7}{20} ×\times 240
= 7 ×\times 12
= 84

Question Type

Answer Box

Variables

Variable nameVariable value
question
There are 360 animals at a rescue shelter. Two-thirds of the animals are dogs and the rest are cats. 35% of the dogs are puppies. How many puppies are at the shelter?
workedSolution
| | | | ----------------------:| -------------------------------------------- | | Number of dogs | \= $\dfrac{2}{3}$ $\times$ 360 | | | \= $\dfrac{2}{3}$ $\times$ 3 $\times$ 120 | | | \= 2 $\times$ 120 = 240 |

| | | | ----------------------:| -------------------------------------------- | | Number of puppies | \= 35% $\times$ 240 | | | \= $\dfrac{35}{100}$ $\times$ 240 | | | \= $\dfrac{7}{20}$ $\times$ 240 | | | \= 7 $\times$ 12 | | | \= {{{correctAnswer0}}} |
correctAnswer0
84
prefix0
suffix0
puppies

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
correctAnswer084

puppies

Variant 1

DifficultyLevel

689

Question

There are 480 students at a school.

Three-eighths of the students study music and the rest study art. 45% of the music students play piano.

How many music students play piano?

Worked Solution
Number of music students = 38\dfrac{3}{8} ×\times 480
= 38\dfrac{3}{8} ×\times 8 ×\times 60
= 3 ×\times 60 = 180

Number who play piano = 45% ×\times 180
= 45100\dfrac{45}{100} ×\times 180
= 920\dfrac{9}{20} ×\times 180
= 9 ×\times 9
= 81

Question Type

Answer Box

Variables

Variable nameVariable value
question
There are 480 students at a school. Three-eighths of the students study music and the rest study art. 45% of the music students play piano. How many music students play piano?
workedSolution
| | | | ----------------------:| -------------------------------------------- | | Number of music students | \= $\dfrac{3}{8}$ $\times$ 480 | | | \= $\dfrac{3}{8}$ $\times$ 8 $\times$ 60 | | | \= 3 $\times$ 60 = 180 |

| | | | ----------------------:| -------------------------------------------- | | Number who play piano | \= 45% $\times$ 180 | | | \= $\dfrac{45}{100}$ $\times$ 180 | | | \= $\dfrac{9}{20}$ $\times$ 180 | | | \= 9 $\times$ 9 | | | \= {{{correctAnswer0}}} |
correctAnswer0
81
prefix0
suffix0
students

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
correctAnswer081

students

Variant 2

DifficultyLevel

691

Question

There are 560 books in a library.

Three-sevenths of the books are fiction and the rest are non-fiction. 15% of the fiction books are mysteries.

How many mystery books are in the library?

Worked Solution
Number of fiction books = 37\dfrac{3}{7} ×\times 560
= 37\dfrac{3}{7} ×\times 7 ×\times 80
= 3 ×\times 80 = 240

Number of mystery books = 15% ×\times 240
= 15100\dfrac{15}{100} ×\times 240
= 320\dfrac{3}{20} ×\times 240
= 3 ×\times 12
= 36

Question Type

Answer Box

Variables

Variable nameVariable value
question
There are 560 books in a library. Three-sevenths of the books are fiction and the rest are non-fiction. 15% of the fiction books are mysteries. How many mystery books are in the library?
workedSolution
| | | | ----------------------:| -------------------------------------------- | | Number of fiction books | \= $\dfrac{3}{7}$ $\times$ 560 | | | \= $\dfrac{3}{7}$ $\times$ 7 $\times$ 80 | | | \= 3 $\times$ 80 = 240 |

| | | | ----------------------:| -------------------------------------------- | | Number of mystery books | \= 15% $\times$ 240 | | | \= $\dfrac{15}{100}$ $\times$ 240 | | | \= $\dfrac{3}{20}$ $\times$ 240 | | | \= 3 $\times$ 12 | | | \= {{{correctAnswer0}}} |
correctAnswer0
36
prefix0
suffix0
mystery books

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

mystery books

Variant 3

DifficultyLevel

693

Question

There are 640 people at a concert.

Five-eighths of the people are adults and the rest are children. 30% of the adults are over 50.

How many adults over 50 are at the concert?

Worked Solution
Number of adults = 58\dfrac{5}{8} ×\times 640
= 58\dfrac{5}{8} ×\times 8 ×\times 80
= 5 ×\times 80 = 400

Number of adults over 50 = 30% ×\times 400
= 30100\dfrac{30}{100} ×\times 400
= 310\dfrac{3}{10} ×\times 400
= 3 ×\times 40
= 120

Question Type

Answer Box

Variables

Variable nameVariable value
question
There are 640 people at a concert. Five-eighths of the people are adults and the rest are children. 30% of the adults are over 50. How many adults over 50 are at the concert?
workedSolution
| | | | ----------------------:| -------------------------------------------- | | Number of adults | \= $\dfrac{5}{8}$ $\times$ 640 | | | \= $\dfrac{5}{8}$ $\times$ 8 $\times$ 80 | | | \= 5 $\times$ 80 = 400 |

| | | | ----------------------:| -------------------------------------------- | | Number of adults over 50 | \= 30% $\times$ 400 | | | \= $\dfrac{30}{100}$ $\times$ 400 | | | \= $\dfrac{3}{10}$ $\times$ 400 | | | \= 3 $\times$ 40 | | | \= {{{correctAnswer0}}} |
correctAnswer0
120
prefix0
suffix0
adults over 50

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
correctAnswer0120

adults over 50

Variant 4

DifficultyLevel

695

Question

There are 900 workers in an office building.

Four-ninths of the workers are on the upper floors and the rest are on the lower floors. 55% of the upper floor workers are in the finance department.

How many upper floor workers are in finance?

Worked Solution
Number of upper floor workers = 49\dfrac{4}{9} ×\times 900
= 49\dfrac{4}{9} ×\times 9 ×\times 100
= 4 ×\times 100 = 400

Number in finance = 55% ×\times 400
= 55100\dfrac{55}{100} ×\times 400
= 1120\dfrac{11}{20} ×\times 400
= 11 ×\times 20
= 220

Question Type

Answer Box

Variables

Variable nameVariable value
question
There are 900 workers in an office building. Four-ninths of the workers are on the upper floors and the rest are on the lower floors. 55% of the upper floor workers are in the finance department. How many upper floor workers are in finance?
workedSolution
| | | | --------------------------:| -------------------------------------------- | | Number of upper floor workers | \= $\dfrac{4}{9}$ $\times$ 900 | | | \= $\dfrac{4}{9}$ $\times$ 9 $\times$ 100 | | | \= 4 $\times$ 100 = 400 |

| | | | --------------------------:| -------------------------------------------- | | Number in finance | \= 55% $\times$ 400 | | | \= $\dfrac{55}{100}$ $\times$ 400 | | | \= $\dfrac{11}{20}$ $\times$ 400 | | | \= 11 $\times$ 20 | | | \= {{{correctAnswer0}}} |
correctAnswer0
220
prefix0
suffix0
upper floor workers

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
correctAnswer0220

upper floor workers

Tags

  • staging_suejones