Number_gap-2026_717

Question

{{{question}}}

Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

717

Question

500 tickets were sold for a concert.

The ratio of adult tickets to child tickets was 3:2.

40 adult tickets and 20 child tickets were refunded due to bad weather.

What is the new ratio of adult to child tickets? Give your answer as a fraction in simplest form.

Worked Solution
Adult tickets = 35\dfrac{3}{5} ×\times 500 = 300
Child tickets = 25\dfrac{2}{5} ×\times 500 = 200

Adult tickets after refunds = 300 − 40 = 260
Child tickets after refunds = 200 − 20 = 180

New ratio = 260180\dfrac{260}{180}
= 139\dfrac{13}{9}

Question Type

Answer Box

Variables

Variable nameVariable value
question
500 tickets were sold for a concert. The ratio of adult tickets to child tickets was 3:2. 40 adult tickets and 20 child tickets were refunded due to bad weather. What is the new ratio of adult to child tickets? Give your answer as a fraction in simplest form.
workedSolution
| | | | ----------------------:| -------------------------------------------- | | Adult tickets | \= $\dfrac{3}{5}$ $\times$ 500 = 300 | | Child tickets | \= $\dfrac{2}{5}$ $\times$ 500 = 200 |

| | | | ----------------------:| -------------------------------------------- | | Adult tickets after refunds | \= 300 − 40 = 260 | | Child tickets after refunds | \= 200 − 20 = 180 |

| | | | ----------------------:| -------------------------------------------- | | New ratio | \= $\dfrac{260}{180}$ | | | \= {{{correctAnswer0}}} |
correctAnswer0
$\dfrac{13}{9}$
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
correctAnswer0$\dfrac{13}{9}$

Variant 1

DifficultyLevel

719

Question

A nursery has 400 plants.

The ratio of flowering to non-flowering plants was 3:2.

20 flowering and 40 non-flowering plants were sold.

What is the new ratio of flowering to non-flowering plants? Give your answer as a fraction in simplest form.

Worked Solution
Flowering plants = 35\dfrac{3}{5} ×\times 400 = 240
Non-flowering plants = 25\dfrac{2}{5} ×\times 400 = 160

Flowering after sales = 240 − 20 = 220
Non-flowering after sales = 160 − 40 = 120

New ratio = 220120\dfrac{220}{120}
= 116\dfrac{11}{6}

Question Type

Answer Box

Variables

Variable nameVariable value
question
A nursery has 400 plants. The ratio of flowering to non-flowering plants was 3:2. 20 flowering and 40 non-flowering plants were sold. What is the new ratio of flowering to non-flowering plants? Give your answer as a fraction in simplest form.
workedSolution
| | | | ----------------------:| -------------------------------------------- | | Flowering plants | \= $\dfrac{3}{5}$ $\times$ 400 = 240 | | Non-flowering plants | \= $\dfrac{2}{5}$ $\times$ 400 = 160 |

| | | | ----------------------:| -------------------------------------------- | | Flowering after sales | \= 240 − 20 = 220 | | Non-flowering after sales | \= 160 − 40 = 120 |

| | | | ----------------------:| -------------------------------------------- | | New ratio | \= $\dfrac{220}{120}$ | | | \= {{{correctAnswer0}}} |
correctAnswer0
$\dfrac{11}{6}$
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
correctAnswer0$\dfrac{11}{6}$

Variant 2

DifficultyLevel

721

Question

A bag contains 560 marbles.

The ratio of red to blue marbles was 3:4.

15 red and 25 blue marbles were removed.

What is the new ratio of red to blue marbles? Give your answer as a fraction in simplest form.

Worked Solution
Red marbles = 37\dfrac{3}{7} ×\times 560 = 240
Blue marbles = 47\dfrac{4}{7} ×\times 560 = 320

Red marbles remaining = 240 − 15 = 225
Blue marbles remaining = 320 − 25 = 295

New ratio = 225295\dfrac{225}{295}
= 5×455×59\dfrac{5 \times 45}{5 \times 59}
= 4559\dfrac{45}{59}

Question Type

Answer Box

Variables

Variable nameVariable value
question
A bag contains 560 marbles. The ratio of red to blue marbles was 3:4. 15 red and 25 blue marbles were removed. What is the new ratio of red to blue marbles? Give your answer as a fraction in simplest form.
workedSolution
| | | | ----------------------:| -------------------------------------------- | | Red marbles | \= $\dfrac{3}{7}$ $\times$ 560 = 240 | | Blue marbles | \= $\dfrac{4}{7}$ $\times$ 560 = 320 |

| | | | ----------------------:| -------------------------------------------- | | Red marbles remaining | \= 240 − 15 = 225 | | Blue marbles remaining | \= 320 − 25 = 295 |

| | | | ----------------------:| -------------------------------------------- | | New ratio | \= $\dfrac{225}{295}$ | | | \= $\dfrac{5 \times 45}{5 \times 59}$ | | | \= {{{correctAnswer0}}} |
correctAnswer0
$\dfrac{45}{59}$
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
correctAnswer0$\dfrac{45}{59}$

Variant 3

DifficultyLevel

723

Question

A gym has 630 members.

The ratio of male to female members was 4:5.

45 male and 30 female memberships lapsed.

What is the new ratio of male to female members? Give your answer as a fraction in simplest form.

Worked Solution
Male members = 49\dfrac{4}{9} ×\times 630 = 280
Female members = 59\dfrac{5}{9} ×\times 630 = 350

Male members remaining = 280 − 45 = 235
Female members remaining = 350 − 30 = 320

New ratio = 235320\dfrac{235}{320}
= 5×475×64\dfrac{5 \times 47}{5 \times 64}
= 4764\dfrac{47}{64}

Question Type

Answer Box

Variables

Variable nameVariable value
question
A gym has 630 members. The ratio of male to female members was 4:5. 45 male and 30 female memberships lapsed. What is the new ratio of male to female members? Give your answer as a fraction in simplest form.
workedSolution
| | | | ----------------------:| -------------------------------------------- | | Male members | \= $\dfrac{4}{9}$ $\times$ 630 = 280 | | Female members | \= $\dfrac{5}{9}$ $\times$ 630 = 350 |

| | | | ----------------------:| -------------------------------------------- | | Male members remaining | \= 280 − 45 = 235 | | Female members remaining | \= 350 − 30 = 320 |

| | | | ----------------------:| ---------------------- | | New ratio | \= $\dfrac{235}{320}$ | | | \= $\dfrac{5 \times 47}{5 \times 64}$| | |\= {{{correctAnswer0}}}|
correctAnswer0
$\dfrac{47}{64}$
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
correctAnswer0$\dfrac{47}{64}$

Variant 4

DifficultyLevel

725

Question

A warehouse has 800 items.

The ratio of large to small items was 3:5.

60 large and 40 small items were dispatched.

What is the new ratio of large to small items? Give your answer as a fraction in simplest form.

Worked Solution
Large items = 38\dfrac{3}{8} ×\times 800 = 300
Small items = 58\dfrac{5}{8} ×\times 800 = 500

Large items remaining = 300 − 60 = 240
Small items remaining = 500 − 40 = 460

New ratio = 240460\dfrac{240}{460}
= 20×1220×23\dfrac{20 \times 12}{20 \times 23}
= 1223\dfrac{12}{23}

Question Type

Answer Box

Variables

Variable nameVariable value
question
A warehouse has 800 items. The ratio of large to small items was 3:5. 60 large and 40 small items were dispatched. What is the new ratio of large to small items? Give your answer as a fraction in simplest form.
workedSolution
| | | | ----------------------:| -------------------------------------------- | | Large items | \= $\dfrac{3}{8}$ $\times$ 800 = 300 | | Small items | \= $\dfrac{5}{8}$ $\times$ 800 = 500 |

| | | | ----------------------:| -------------------------------------------- | | Large items remaining | \= 300 − 60 = 240 | | Small items remaining | \= 500 − 40 = 460 |

| | | | ----------:| -------------------------------------------- | | New ratio | \= $\dfrac{240}{460}$ | | | \= $\dfrac{20 \times 12}{20 \times 23}$ | | | \= {{{correctAnswer0}}} |
correctAnswer0
$\dfrac{12}{23}$
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
correctAnswer0$\dfrac{12}{23}$

Tags

  • staging _suejones