Algebra, NAPX9-TLF-CA40 SA v3

Question

{{{question}}}

Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

740

Question

May created liquid sanitiser by mixing the four liquids: water, alcohol, solution A and solution B.

She makes 650 litres of the sanitiser according to the following instructions:

  • 60% of the mixture is water.

  • Solution A is used in the same volume as Solution B.

  • The volume of alcohol is three times the volume of Solution B.

How many litres of Solution A are required to make 650 litres of the sanitiser?

Worked Solution
Volume of water = 60%×65060\% \times 650
= 390 litres

Volume of remaining liquids
= 650 −- 390
= 260 litres

Let  x\ \large x = volume of Solution A
x\large x + x\large x + 3x\large x = 260
5x5\large x = 260
∴ x\therefore \ \large x = 52 litres

Question Type

Answer Box

Variables

Variable nameVariable value
question
May created liquid sanitiser by mixing the four liquids: water, alcohol, solution A and solution B. She makes 650 litres of the sanitiser according to the following instructions: * 60% of the mixture is water. * Solution A is used in the same volume as Solution B. * The volume of alcohol is three times the volume of Solution B. How many litres of Solution A are required to make 650 litres of the sanitiser?
workedSolution
| | | | ------------: | ---------- | | Volume of water | \= $60\% \times 650$| | | \= 390 litres |

sm_nogap Volume of remaining liquids
>>| | | ---------- | | \= 650 $-$ 390 | | \= 260 litres |

sm_nogap Let $\ \large x$ = volume of Solution A
| | | | ------------: | ---------- | | $\large x$ + $\large x$ + 3$\large x$ | \= 260 | | $5\large x$ | \= 260 | | $\therefore \ \large x$ | \= {{{correctAnswer0}}} {{{suffix0}}} |
correctAnswer0
52
prefix0
suffix0
litres

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
correctAnswer052

litres

Variant 1

DifficultyLevel

749

Question

Justine created garden soil by mixing the four ingredients: compost, peat moss, cow manure and vermiculite.

She makes 450 kilograms of the garden soil according to the following instructions:

  • 30% of the mixture is compost.

  • peat moss is used in the same amount as vermiculite.

  • The amount of cow manure is one-third of the amount of the peat moss.

How many kilograms of peat moss are required to make 450 kilograms of the garden soil?

Worked Solution
Amount of compost = 30%×45030\% \times 450
= 135 kilograms

Amount of remaining ingredients
= 450 −- 135
= 315 kilograms

Let  x\ \large x = amount of peat moss
x\large x + x\large x + 13x\dfrac{1}{3}\large x = 315
73x\dfrac{7}{3}\large x = 315
x\large x = 315 × 37\times\ \dfrac{3}{7}
∴ x\therefore \ \large x = 135 kilograms

Question Type

Answer Box

Variables

Variable nameVariable value
question
Justine created garden soil by mixing the four ingredients: compost, peat moss, cow manure and vermiculite. She makes 450 kilograms of the garden soil according to the following instructions: * 30% of the mixture is compost. * peat moss is used in the same amount as vermiculite. * The amount of cow manure is one-third of the amount of the peat moss. How many kilograms of peat moss are required to make 450 kilograms of the garden soil?
workedSolution
| | | | ------------: | ---------- | | Amount of compost | \= $30\% \times 450$| | | \= 135 kilograms |

sm_nogap Amount of remaining ingredients
>>| | | ---------- | | \= 450 $-$ 135 | | \= 315 kilograms |

sm_nogap Let $\ \large x$ = amount of peat moss
| | | | ------------: | ---------- | | $\large x$ + $\large x$ + $\dfrac{1}{3}\large x$ | \= 315 | | $\dfrac{7}{3}\large x$ | \= 315 | | $\large x$ | = 315 $\times\ \dfrac{3}{7}$ | | $\therefore \ \large x$ | \= {{{correctAnswer0}}} {{{suffix0}}} |
correctAnswer0
135
prefix0
suffix0
kilograms

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
correctAnswer0135

kilograms

Variant 2

DifficultyLevel

742

Question

Mel made a jug of green smoothies for her friends by mixing the four ingredients: kale, avocado, ice and almond milk.

She makes 4 litres of the green smoothie according to the following instructions:

  • 50% of the mixture is avocado.

  • Almond milk is used in the same volume as ice.

  • The volume of kale is two times the volume of ice.

How many millilitres of almond milk are required to make 4 litres of the green smoothie?

Worked Solution
Volume of avocado = 50%×450\% \times 4
= 2 litres

Volume of remaining ingredients
= 4 −- 2
= 2 litres
= 2000 millilitres

Let  x\ \large x = volume of almond milk
x\large x + x\large x + 2x\large x = 2000
4x4\large x = 2000
∴ x\therefore \ \large x = 500 millilitres

Question Type

Answer Box

Variables

Variable nameVariable value
question
Mel made a jug of green smoothies for her friends by mixing the four ingredients: kale, avocado, ice and almond milk. She makes 4 litres of the green smoothie according to the following instructions: * 50% of the mixture is avocado. * Almond milk is used in the same volume as ice. * The volume of kale is two times the volume of ice. How many millilitres of almond milk are required to make 4 litres of the green smoothie?
workedSolution
| | | | ------------: | ---------- | | Volume of avocado | \= $50\% \times 4$| | | \= 2 litres |

sm_nogap Volume of remaining ingredients
>>| | | ---------- | | \= 4 $-$ 2 | | \= 2 litres | | \= 2000 millilitres |

sm_nogap Let $\ \large x$ = volume of almond milk
| | | | ------------: | ---------- | | $\large x$ + $\large x$ + 2$\large x$ | \= 2000 | | $4\large x$ | \= 2000 | | $\therefore \ \large x$ | \= {{{correctAnswer0}}} {{{suffix0}}} |
correctAnswer0
500
prefix0
suffix0
millilitres

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
correctAnswer0500

millilitres

Variant 3

DifficultyLevel

746

Question

Jerry was preparing to lay a small cement slab in his back yard.

He mixed the four ingredients: cement, rock, sand and water.

Jerry makes 50 kilograms of the cement mix according to the following instructions:

  • 40% of the mixture is rock.

  • the same mass of sand and water is used.

  • The mass of cement is half the mass of sand.

How many kilograms of sand are required to make 50 kilograms of the cement mix?

Worked Solution
Mass of rock = 40%×5040\% \times 50
= 20 kilograms

Mass of remaining ingredients
= 50 −- 20
= 30 kilograms

Let  x\ \large x = mass of sand
x\large x + x\large x + 12x\dfrac{1}{2}\large x = 30
52x\dfrac{5}{2}\large x = 30
x\large x = 30 × 25\times\ \dfrac{2}{5}
∴ x\therefore \ \large x = 12 kilograms

Question Type

Answer Box

Variables

Variable nameVariable value
question
Jerry was preparing to lay a small cement slab in his back yard. He mixed the four ingredients: cement, rock, sand and water. Jerry makes 50 kilograms of the cement mix according to the following instructions: * 40% of the mixture is rock. * the same mass of sand and water is used. * The mass of cement is half the mass of sand. How many kilograms of sand are required to make 50 kilograms of the cement mix?
workedSolution
| | | | ------------: | ---------- | | Mass of rock | \= $40\% \times 50$| | | \= 20 kilograms |

sm_nogap Mass of remaining ingredients
>>| | | ---------- | | \= 50 $-$ 20 | | \= 30 kilograms |

sm_nogap Let $\ \large x$ = mass of sand
| | | | ------------: | ---------- | | $\large x$ + $\large x$ + $\dfrac{1}{2}\large x$ | \= 30 | | $\dfrac{5}{2}\large x$ | \= 30 | | $\large x$ | = 30 $\times\ \dfrac{2}{5}$ | | $\therefore \ \large x$ | \= {{{correctAnswer0}}} {{{suffix0}}} |
correctAnswer0
12
prefix0
suffix0
kilograms

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

kilograms

Variant 4

DifficultyLevel

748

Question

Julie is creating an exercise program.

She includes the four exercises: burpees, squats, push ups and box jumps.

The program requires 420 individual repetitions of the exercises given the following instructions:

  • 20% of the repetitions are push ups.

  • squat repetitions are double burpee repetitions.

  • box jump repetitions are half burpee repetitions.

How many repetitions of burpees are included in Julie's 420 repetition exercise program?

Worked Solution
Push up repetitions = 20%×42020\% \times 420
= 84 repetitions

Repetitions of remaining exercises
= 420 −- 84
= 336 repetitions

Let  x\ \large x = burpee repetitions
2x2\large x + x\large x + 12x\dfrac{1}{2}\large x = 336
72x\dfrac{7}{2}\large x = 336
x\large x = 336 × 27\times\ \dfrac{2}{7}
∴ x\therefore \ \large x = 96 repetitions

Question Type

Answer Box

Variables

Variable nameVariable value
question
Julie is creating an exercise program. She includes the four exercises: burpees, squats, push ups and box jumps. The program requires 420 individual repetitions of the exercises given the following instructions: * 20% of the repetitions are push ups. * squat repetitions are double burpee repetitions. * box jump repetitions are half burpee repetitions. How many repetitions of burpees are included in Julie's 420 repetition exercise program?
workedSolution
| | | | ------------: | ---------- | | Push up repetitions | \= $20\% \times 420$| | | \= 84 repetitions |

sm_nogap Repetitions of remaining exercises
>>| | | ---------- | | \= 420 $-$ 84 | | \= 336 repetitions |

sm_nogap Let $\ \large x$ = burpee repetitions
| | | | ------------: | ---------- | | $2\large x$ + $\large x$ + $\dfrac{1}{2}\large x$ | \= 336 | | $\dfrac{7}{2}\large x$ | \= 336 | | $\large x$ | = 336 $\times\ \dfrac{2}{7}$ | | $\therefore \ \large x$ | \= {{{correctAnswer0}}} {{{suffix0}}} |
correctAnswer0
96
prefix0
suffix0
repetitions

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
correctAnswer096

repetitions

Variant 5

DifficultyLevel

750

Question

Kira is organising her school's athletics carnival.

In the morning session she rotates the Year 9 participants through 4 activities: 100 metres sprint, discus, shot put and high jump.

The morning session is 2 hours long and time is allocated using the following constraints:

  • 40% of the total time allocation is taken up by high jump.

  • discus and shot put are allocated an equal amount time.

  • The 100 metres sprint is allocated one quarter the amount of time of shot put.

What is the amount of time, in minutes, allocated to shot put during the 2 hour morning session?

Worked Solution

2 hours ⇒\Rightarrow 120 minures
High jump time allocation = 40%×12040\% \times 120
= 48 minutes

Time allocation of remaining activities
= 120 −- 48
= 72 minutes

Let  x\ \large x = shot put time allocation
x\large x + x\large x + 14x\dfrac{1}{4}\large x = 72
94x\dfrac{9}{4}\large x = 72
x\large x = 72 × 49\times\ \dfrac{4}{9}
∴ x\therefore \ \large x = 32 minutes

Question Type

Answer Box

Variables

Variable nameVariable value
question
Kira is organising her school's athletics carnival. In the morning session she rotates the Year 9 participants through 4 activities: 100 metres sprint, discus, shot put and high jump. The morning session is 2 hours long and time is allocated using the following constraints: * 40% of the total time allocation is taken up by high jump. * discus and shot put are allocated an equal amount time. * The 100 metres sprint is allocated one quarter the amount of time of shot put. What is the amount of time, in minutes, allocated to shot put during the 2 hour morning session?
workedSolution
2 hours $\Rightarrow$ 120 minures
| | | | ------------: | ---------- | | High jump time allocation | \= $40\% \times 120$| | | \= 48 minutes |

sm_nogap Time allocation of remaining activities
>>| | | ---------- | | \= 120 $-$ 48 | | \= 72 minutes |

sm_nogap Let $\ \large x$ = shot put time allocation
| | | | ------------: | ---------- | | $\large x$ + $\large x$ + $\dfrac{1}{4}\large x$ | \= 72 | | $\dfrac{9}{4}\large x$ | \= 72 | | $\large x$ | = 72 $\times\ \dfrac{4}{9}$ | | $\therefore \ \large x$ | \= {{{correctAnswer0}}} {{{suffix0}}} |
correctAnswer0
32
prefix0
suffix0
minutes

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
correctAnswer032

minutes

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