Algebra, NAPX-G4-NC31 SA

Question

{{{question}}}

Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

642

Question

Manou was cooking a defrosted chicken in his oven and checking its temperature every 7 minutes.

The first temperature taken was −8.2°C.

The second temperature was 4.2°C.

The third measurement showed that the temperature had increased one and a half times the previous increase.

What was the third temperature?

Worked Solution
1st increase = 4.2 − (−8.2)4.2\ −\ (−8.2)
= 4.2+8.24.2+8.2
= 12.4

2nd increase = 1.5×12.41.5×12.4
= 1×12.4+0.5×12.41×12.4+0.5×12.4
= 12.4+6.212.4+6.2
= 18.6

∴\therefore Third temp = 4.2+18.64.2+18.6
= 22.8°\degreeC

Question Type

Answer Box

Variables

Variable nameVariable value
question
Manou was cooking a defrosted chicken in his oven and checking its temperature every 7 minutes. The first temperature taken was −8.2°C. The second temperature was 4.2°C. The third measurement showed that the temperature had increased one and a half times the previous increase. What was the third temperature?
workedSolution
| | | | -------------: | ---------- | | 1st increase | \= $4.2\ −\ (−8.2)$ | | | \= $4.2+8.2$ | | | \= 12.4 |

| | | | ------------: | ---------- | | 2nd increase | \= $1.5×12.4$ | | | \= $1×12.4+0.5×12.4$ | | | \= $12.4+6.2$ | | | \= 18.6 |

| | | | ------------: | ---------- | | $\therefore$ Third temp | \= $4.2+18.6$ | | | \= {{{correctAnswer0}}}{{{suffix0}}} |
correctAnswer0
22.8
prefix0
suffix0
$\degree$C

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
correctAnswer022.8

°\degreeC

Variant 1

DifficultyLevel

650

Question

Marion was cooking a defrosted Viking steak in her oven and checking its temperature every 10 minutes.

The first temperature taken was −2.8°C.

The second temperature was 13.6°C.

The third measurement showed that the temperature had increased one and a quarter times the previous increase.

What was the third temperature?

Worked Solution
1st increase = 13.6 − (−2.8)13.6\ −\ (−2.8)
= 13.6+2.813.6+2.8
= 16.4

2nd increase = 1.25×16.41.25×16.4
= 1×16.4+0.25×16.41×16.4+0.25×16.4
= 16.4+4.116.4+4.1
= 20.5

∴\therefore Third temp = 13.6+20.513.6+20.5
= 34.1°\degreeC

Question Type

Answer Box

Variables

Variable nameVariable value
question
Marion was cooking a defrosted Viking steak in her oven and checking its temperature every 10 minutes. The first temperature taken was −2.8°C. The second temperature was 13.6°C. The third measurement showed that the temperature had increased one and a quarter times the previous increase. What was the third temperature?
workedSolution
| | | | -------------: | ---------- | | 1st increase | \= $13.6\ −\ (−2.8)$ | | | \= $13.6+2.8$ | | | \= 16.4 |

| | | | ------------: | ---------- | | 2nd increase | \= $1.25×16.4$ | | | \= $1×16.4+0.25×16.4$ | | | \= $16.4+4.1$ | | | \= 20.5 |

| | | | ------------: | ---------- | | $\therefore$ Third temp | \= $13.6+20.5$ | | | \= {{{correctAnswer0}}}{{{suffix0}}} |
correctAnswer0
34.1
prefix0
suffix0
$\degree$C

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
correctAnswer034.1

°\degreeC

Variant 2

DifficultyLevel

701

Question

Adam was cooking a partly frozen lasagne in his oven and checking its temperature every 5 minutes.

The first temperature taken was −31.4°C.

The second temperature was −13.4°C.

The third measurement showed that the temperature had increased two and a one tenth times the previous increase.

What was the third temperature?

Worked Solution
1st increase = −13.4 − (−31.4)−13.4\ −\ (−31.4)
= −13.4+31.4−13.4+31.4
= 18

2nd increase = 2.1×182.1×18
= 2×18+0.1×182×18+0.1×18
= 36+1.836+1.8
= 37.8

∴\therefore Third temp = −13.4+37.8−13.4+37.8
= 24.4°\degreeC

Question Type

Answer Box

Variables

Variable nameVariable value
question
Adam was cooking a partly frozen lasagne in his oven and checking its temperature every 5 minutes. The first temperature taken was −31.4°C. The second temperature was −13.4°C. The third measurement showed that the temperature had increased two and a one tenth times the previous increase. What was the third temperature?
workedSolution
| | | | -------------: | ---------- | | 1st increase | \= $−13.4\ −\ (−31.4)$ | | | \= $−13.4+31.4$ | | | \= 18 |

| | | | ------------: | ---------- | | 2nd increase | \= $2.1×18$ | | | \= $2×18+0.1×18$ | | | \= $36+1.8$ | | | \= 37.8 |

| | | | ------------: | ---------- | | $\therefore$ Third temp | \= $−13.4+37.8$ | | | \= {{{correctAnswer0}}}{{{suffix0}}} |
correctAnswer0
24.4
prefix0
suffix0
$\degree$C

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
correctAnswer024.4

°\degreeC

Variant 3

DifficultyLevel

695

Question

Einstein heated a beaker filled with ice water using a Bunsen burner. He measured the temperature every 30 seconds.

The third temperature taken was −31.1°C.

The fourth temperature was −9.9°C.

The fifth measurement showed that the temperature had increased three and a quarter times the previous increase.

What was the fifth temperature?

Worked Solution
1st increase = −9.9 − (−31.1)−9.9\ −\ (−31.1)
= −9.9+31.1−9.9+31.1
= 21.2

2nd increase = 3.25×21.23.25×21.2
= 3×21.2+0.25×21.23×21.2+0.25×21.2
= 63.6+5.363.6+5.3
= 68.9

∴\therefore Fifth temp = −9.9+68.9−9.9+68.9
= 59°\degreeC

Question Type

Answer Box

Variables

Variable nameVariable value
question
Einstein heated a beaker filled with ice water using a Bunsen burner. He measured the temperature every 30 seconds. The third temperature taken was −31.1°C. The fourth temperature was −9.9°C. The fifth measurement showed that the temperature had increased three and a quarter times the previous increase. What was the fifth temperature?
workedSolution
| | | | -------------: | ---------- | | 1st increase | \= $−9.9\ −\ (−31.1)$ | | | \= $−9.9+31.1$ | | | \= 21.2 |

| | | | ------------: | ---------- | | 2nd increase | \= $3.25×21.2$ | | | \= $3×21.2+0.25×21.2$ | | | \= $63.6+5.3$ | | | \= 68.9 |

| | | | ------------: | ---------- | | $\therefore$ Fifth temp | \= $−9.9+68.9$ | | | \= {{{correctAnswer0}}}{{{suffix0}}} |
correctAnswer0
59
prefix0
suffix0
$\degree$C

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
correctAnswer059

°\degreeC

Variant 4

DifficultyLevel

690

Question

Donna had baked a cheesecake and put it in the freezer to cool. She checked the temperature of the cheesecake every 45 minutes.

The first temperature taken was 180.8°C.

The second temperature was 84.6°C.

The third measurement showed that the temperature had decreased one and a half times the previous decrease.

What was the third temperature?

Worked Solution
1st decrease = 180.8 − 84.6180.8\ −\ 84.6
= 96.2

2nd decrease = 1.5×96.21.5×96.2
= 1×96.2+0.5×96.21×96.2+0.5×96.2
= 96.2+48.196.2+48.1
= 144.3

∴\therefore Third temp = 84.6 − 144.3
= −59.7°\degreeC

Question Type

Answer Box

Variables

Variable nameVariable value
question
Donna had baked a cheesecake and put it in the freezer to cool. She checked the temperature of the cheesecake every 45 minutes. The first temperature taken was 180.8°C. The second temperature was 84.6°C. The third measurement showed that the temperature had decreased one and a half times the previous decrease. What was the third temperature?
workedSolution
| | | | -------------: | ---------- | | 1st decrease| \= $180.8\ −\ 84.6$ | | | \= 96.2 |

| | | | ------------: | ---------- | | 2nd decrease | \= $1.5×96.2$ | | | \= $1×96.2+0.5×96.2$ | | | \= $96.2+48.1$ | | | \= 144.3 |

| | | | ------------: | ---------- | | $\therefore$ Third temp | \= 84.6 − 144.3 | | | \= {{{correctAnswer0}}}{{{suffix0}}} |
correctAnswer0
−59.7
prefix0
suffix0
$\degree$C

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
correctAnswer0−59.7

°\degreeC

Variant 5

DifficultyLevel

693

Question

George was testing the temperature of his melting chocolate icecream every 30 seconds.

The first temperature taken was −18.7°C.

The second temperature was −15.3°C.

The third measurement showed that the temperature had increased one and a half times the previous increase.

What was the third temperature?

Worked Solution
1st increase = −15.3 − (−18.7)−15.3\ −\ (−18.7)
= −15.3+18.7−15.3+18.7
= 3.4

2nd increase = 1.5×3.41.5×3.4
= 1×3.4+0.5×3.41×3.4+0.5×3.4
= 3.4+1.73.4+1.7
= 5.1

∴\therefore Third temp = −15.3+5.1−15.3+5.1
= −10.2°\degreeC

Question Type

Answer Box

Variables

Variable nameVariable value
question
George was testing the temperature of his melting chocolate icecream every 30 seconds. The first temperature taken was −18.7°C. The second temperature was −15.3°C. The third measurement showed that the temperature had increased one and a half times the previous increase. What was the third temperature?
workedSolution
| | | | -------------: | ---------- | | 1st increase | \= $−15.3\ −\ (−18.7)$ | | | \= $−15.3+18.7$ | | | \= 3.4 |

| | | | ------------: | ---------- | | 2nd increase | \= $1.5×3.4$ | | | \= $1×3.4+0.5×3.4$ | | | \= $3.4+1.7$ | | | \= 5.1 |

| | | | ------------: | ---------- | | $\therefore$ Third temp | \= $−15.3+5.1$ | | | \= {{{correctAnswer0}}}{{{suffix0}}} |
correctAnswer0
−10.2
prefix0
suffix0
$\degree$C

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
correctAnswer0−10.2

°\degreeC

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