Algebra, NAPX-H3-CA29 SA

Question

{{{question}}}

Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

703

Question

Ember is six years younger than Keenak.

Starla is thirteen years older than twice Keenak's age.

The sum of all three ages is 63.

How old is Starla?

Worked Solution

Strategy one:

Try some educated guesses:

If Ember is 7,

Total of ages = 7 + 13 + 39 = 59

If Ember is 8,

Total of ages = 8 + 14 + 41 = 63 ✓\checkmark


Strategy two (using algebra):

Express the information into 3 equations,
EE = K − 6 ... (1)K \ −\ 6 \ ... \ (1)
SS = 2K+13 … (2)2K+13 \ … \ (2)
E+K+SE+K+S = 63 ...  (3)\ (3)

Substitute (1) and (2) into (3)
K − 6+K+2K+13K\ −\ 6+K+2K+13 = 63
4K4K = 56
KK = 14

∴\therefore Starla's age = 2×14+132×14+13
= 41

Question Type

Answer Box

Variables

Variable nameVariable value
question
Ember is six years younger than Keenak. Starla is thirteen years older than twice Keenak's age. The sum of all three ages is 63. How old is Starla?
workedSolution
Strategy one: Try some educated guesses: If Ember is 7, Total of ages = 7 + 13 + 39 = 59 If Ember is 8, Total of ages = 8 + 14 + 41 = 63 $\checkmark$
Strategy two (using algebra): Express the information into 3 equations,
>| | | | ------------: | ---------- | | $E$ | \= $K \ −\ 6 \ ... \ (1)$ | | $S$ | \= $2K+13 \ … \ (2)$ | | $E+K+S$ | \= 63 ... $\ (3)$ |

Substitute (1) and (2) into (3)
>| | | | -------------: | ---------- | | $K\ −\ 6+K+2K+13$ | \= 63 | | $4K$ | \= 56 | | $K$ | \= 14 |

| | | | ------------- | ---------- | | $\therefore$ Starla's age | \= $2×14+13$ | | | \= {{{correctAnswer0}}} |
correctAnswer0
41
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
correctAnswer041

Variant 1

DifficultyLevel

705

Question

Michaela is four years younger than Brian.

Cormac is ten years older than twice Brian's age.

The sum of all three ages is 86.

How old is Cormac?

Worked Solution

Strategy one:

Try some educated guesses:

If Michaela is 14,

Total of ages = 14 + 18 + 46 = 68

If Michaela is 16,

Total of ages = 16 + 20 + 50 = 86 ✓\checkmark


Strategy two (using algebra):

Express the information into 3 equations,
MM = B − 4 ... (1)B \ −\ 4 \ ... \ (1)
CC = 2B+10 … (2)2B+10 \ … \ (2)
M+B+CM+B+C = 86 ...  (3)\ (3)

Substitute (1) and (2) into (3)
B − 4+B+2B+10B\ −\ 4+B+2B+10 = 86
4B4B = 80
BB = 20

∴\therefore Cormac's age = 2×20+102×20+10
= 50

Question Type

Answer Box

Variables

Variable nameVariable value
question
Michaela is four years younger than Brian. Cormac is ten years older than twice Brian's age. The sum of all three ages is 86. How old is Cormac?
workedSolution
Strategy one: Try some educated guesses: If Michaela is 14, Total of ages = 14 + 18 + 46 = 68 If Michaela is 16, Total of ages = 16 + 20 + 50 = 86 $\checkmark$
Strategy two (using algebra): Express the information into 3 equations,
>| | | | ------------: | ---------- | | $M$ | \= $B \ −\ 4 \ ... \ (1)$ | | $C$ | \= $2B+10 \ … \ (2)$ | | $M+B+C$ | \= 86 ... $\ (3)$ |

Substitute (1) and (2) into (3)
>| | | | -------------: | ---------- | | $B\ −\ 4+B+2B+10$ | \= 86 | | $4B$ | \= 80 | | $B$ | \= 20 |

| | | | ------------- | ---------- | | $\therefore$ Cormac's age | \= $2×20+10$ | | | \= {{{correctAnswer0}}} |
correctAnswer0
50
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
correctAnswer050

Variant 2

DifficultyLevel

720

Question

Abbie is five years younger than Bert.

Ernie is twenty years younger than three times Bert's age.

The sum of all three ages is 50.

How old is Ernie?

Worked Solution

Strategy one:

Try some educated guesses:

If Abbie is 5,

Total of ages = 5 + 10 + 10 = 25

If Abbie is 10,

Total of ages = 10 + 15 + 25 = 50 ✓\checkmark


Strategy two (using algebra):

Express the information into 3 equations,
AA = B − 5 ... (1)B \ −\ 5 \ ... \ (1)
EE = 3B  − 20 … (2)3B\ \ − \ 20 \ … \ (2)
A+B+EA+B+E = 50 ...  (3)\ (3)

Substitute (1) and (2) into (3)
B − 5+B+3B − 20B\ −\ 5+B+3B \ − \ 20 = 50
5B5B = 75
BB = 15

∴\therefore Ernie's age = 3×15 − 203×15 \ − \ 20
= 25

Question Type

Answer Box

Variables

Variable nameVariable value
question
Abbie is five years younger than Bert. Ernie is twenty years younger than three times Bert's age. The sum of all three ages is 50. How old is Ernie?
workedSolution
Strategy one: Try some educated guesses: If Abbie is 5, Total of ages = 5 + 10 + 10 = 25 If Abbie is 10, Total of ages = 10 + 15 + 25 = 50 $\checkmark$
Strategy two (using algebra): Express the information into 3 equations,
>| | | | ------------: | ---------- | | $A$ | \= $B \ −\ 5 \ ... \ (1)$ | | $E$ | \= $3B\ \ − \ 20 \ … \ (2)$ | | $A+B+E$ | \= 50 ... $\ (3)$ |

Substitute (1) and (2) into (3)
>| | | | -------------: | ---------- | | $B\ −\ 5+B+3B \ − \ 20$ | \= 50 | | $5B$ | \= 75 | | $B$ | \= 15 |

| | | | ------------- | ---------- | | $\therefore$ Ernie's age | \= $3×15 \ − \ 20$ | | | \= {{{correctAnswer0}}} |
correctAnswer0
25
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
correctAnswer025

Variant 3

DifficultyLevel

709

Question

Grace is ten years older than Kelly.

Caroline is four years younger than three times Kelly's age.

The sum of all three ages is 76.

How old is Caroline?

Worked Solution

Strategy one:

Try some educated guesses:

If Grace is 20,

Total of ages = 20 + 10 + 26 = 56

If Grace is 24,

Total of ages = 24 + 14 + 38 = 76 ✓\checkmark


Strategy two (using algebra):

Express the information into 3 equations,
GG = K+10 ... (1)K + 10 \ ... \ (1)
CC = 3K − 4 … (2)3K \ −\ 4 \ … \ (2)
G+K+CG+K+C = 76 ...  (3)\ (3)

Substitute (1) and (2) into (3)
K+10+K+3K − 4K + 10+K+3K \ − \ 4 = 76
5K5K = 70
KK = 14

∴\therefore Caroline's age = 3×14 − 43×14 \ −\ 4
= 38

Question Type

Answer Box

Variables

Variable nameVariable value
question
Grace is ten years older than Kelly. Caroline is four years younger than three times Kelly's age. The sum of all three ages is 76. How old is Caroline?
workedSolution
Strategy one: Try some educated guesses: If Grace is 20, Total of ages = 20 + 10 + 26 = 56 If Grace is 24, Total of ages = 24 + 14 + 38 = 76 $\checkmark$
Strategy two (using algebra): Express the information into 3 equations,
>| | | | ------------: | ---------- | | $G$ | \= $K + 10 \ ... \ (1)$ | | $C$ | \= $3K \ −\ 4 \ … \ (2)$ | | $G+K+C$ | \= 76 ... $\ (3)$ |

Substitute (1) and (2) into (3)
>| | | | -------------: | ---------- | | $K + 10+K+3K \ − \ 4$ | \= 76 | | $5K$ | \= 70 | | $K$ | \= 14 |

| | | | ------------- | ---------- | | $\therefore$ Caroline's age | \= $3×14 \ −\ 4$ | | | \= {{{correctAnswer0}}} |
correctAnswer0
38
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
correctAnswer038

Variant 4

DifficultyLevel

709

Question

Byron is twelve years older than Tennyson.

Eyre is one year younger than twice Tennyson's age.

The sum of all three ages is 23.

How old is Eyre?

Worked Solution

Strategy one:

Try some educated guesses:

If Byron is 14,

Total of ages = 14 + 2 + 3 = 19

If Byron is 15,

Total of ages = 15 + 3 + 5 = 23 ✓\checkmark


Strategy two (using algebra):

Express the information into 3 equations,
BB = TT + 12 ... (1)
EE = 2T −2T\ − 1 ... (2)
B+T+EB + T + E = 23 ... (3)

Substitute (1) and (2) into (3)
T+12+T+2T − 1T + 12 + T + 2T\ −\ 1 = 23
4T4T = 12
TT = 3

∴\therefore Eyre's age = 2 ×\times 3 −- 1
= 5

Question Type

Answer Box

Variables

Variable nameVariable value
question
Byron is twelve years older than Tennyson. Eyre is one year younger than twice Tennyson's age. The sum of all three ages is 23. How old is Eyre?
workedSolution
Strategy one: Try some educated guesses: If Byron is 14, Total of ages = 14 + 2 + 3 = 19 If Byron is 15, Total of ages = 15 + 3 + 5 = 23 $\checkmark$
Strategy two (using algebra): Express the information into 3 equations,
>| | | | ------------: | ---------- | | $B$ | = $T$ + 12 ... (1) | | $E$ | = $2T\ −$ 1 ... (2) | | $B + T + E$ | = 23 ... (3) |

Substitute (1) and (2) into (3)
>| | | | -------------: | ---------- | | $T + 12 + T + 2T\ −\ 1$ | = 23 | | $4T$ | = 12 | | $T$ | = 3 |

| | | | ------------- | ---------- | | $\therefore$ Eyre's age | \= 2 $\times$ 3 $-$ 1 | | | \= {{{correctAnswer0}}} |
correctAnswer0
5
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
correctAnswer05

Variant 5

DifficultyLevel

725

Question

Harry is ten years younger than half Voldermort's age.

Dumbledore is three years younger than twice Voldermort's age.

The sum of all three ages is 162.

How old is Dumbledore?

Worked Solution

Strategy one:

Try some educated guesses:

If Voldermort is 40,

Total of ages = 40 + 10 + 77 = 127

If Voldermort is 50,

Total of ages = 50 + 15 + 97 = 162 ✓\checkmark


Strategy two (using algebra):

Express the information into 3 equations,
HH = O.5V − 10O.5V\ −\ 10 ... (1)
DD = 2V− 3 … (2)2V − \ 3 \ … \ (2)
H+V+DH+V+D = 162 ...  (3)\ (3)

Substitute (1) and (2) into (3)
0.5V − 10+V+2V − 30.5V\ − \ 10+V+2V \ −\ 3 = 162
3.5V3.5V = 175
VV = 50

∴\therefore Dumbledore's age = 2×50 − 32×50\ −\ 3
= 97

Question Type

Answer Box

Variables

Variable nameVariable value
question
Harry is ten years younger than half Voldermort's age. Dumbledore is three years younger than twice Voldermort's age. The sum of all three ages is 162. How old is Dumbledore?
workedSolution
Strategy one: Try some educated guesses: If Voldermort is 40, Total of ages = 40 + 10 + 77 = 127 If Voldermort is 50, Total of ages = 50 + 15 + 97 = 162 $\checkmark$
Strategy two (using algebra): Express the information into 3 equations,
>| | | | ------------: | ---------- | | $H$ | = $O.5V\ −\ 10$ ... (1) | | $D$ | \= $2V − \ 3 \ … \ (2)$ | | $H+V+D$ | \= 162 ... $\ (3)$ |

Substitute (1) and (2) into (3)
>| | | | -------------: | ---------- | | $0.5V\ − \ 10+V+2V \ −\ 3$ | \= 162 | | $3.5V$ | \= 175 | | $V$ | \= 50 |

| | | | ------------- | ---------- | | $\therefore$ Dumbledore's age | \= $2×50\ −\ 3$ | | | \= {{{correctAnswer0}}} |
correctAnswer0
97
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
correctAnswer097

Tags