RAPH14 Q103-105

Question

{{{question}}}

Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

646

Question

John and Steve picked up 35 pizzas for a party.

Steve took 7 more pizzas back to the party than John.

How many pizzas did John take back to the party?

Worked Solution

Strategy one:
John's pizzas = (35 – 7) ÷\div 2
= 28 ÷\div 2
= 14

Strategy two (by trial and error):

John takes less than half  →\rightarrow  try 16

If John 16, Steve 23 →\rightarrow  total = 39 (too high)

If John 15, Steve 22 →\rightarrow  total = 37 (too high)

If John 14, Steve 21 →\rightarrow  total = 35 (correct)

Question Type

Answer Box

Variables

Variable nameVariable value
question
John and Steve picked up 35 pizzas for a party. Steve took 7 more pizzas back to the party than John. How many pizzas did John take back to the party?
workedSolution
sm_nogap Strategy one:
| | | | ------------- | ---------- | | John's pizzas| \= (35 – 7) $\div$ 2 | | | \= 28 $\div$ 2 | | | \= {{{correctAnswer0}}} |

Strategy two (by trial and error): John takes less than half  $\rightarrow$  try 16 If John 16, Steve 23 $\rightarrow$  total = 39 (too high) If John 15, Steve 22 $\rightarrow$  total = 37 (too high) If John 14, Steve 21 $\rightarrow$  total = 35 (correct)
correctAnswer0
14
prefix0
suffix0
pizzas

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
correctAnswer014

pizzas

Variant 1

DifficultyLevel

646

Question

Mark and Ivan went fishing together and caught 26 fish together.

Mark caught 8 more fish than Ivan.

How many fish did Ivan catch?

Worked Solution

Strategy one:
Ivan's fish = (26 – 8) ÷\div 2
= 18 ÷\div 2
= 9

Strategy two (by trial and error):

Ivan catches less than half  →\rightarrow  try 12

If Ivan 12, Mark 20 →\rightarrow  total = 32 (too high)

If Ivan 10, Mark 18 →\rightarrow  total = 28 (too high)

If Ivan 9, Mark 17 →\rightarrow  total = 26 (correct)

Question Type

Answer Box

Variables

Variable nameVariable value
question
Mark and Ivan went fishing together and caught 26 fish together. Mark caught 8 more fish than Ivan. How many fish did Ivan catch?
workedSolution
sm_nogap Strategy one:
| | | | ------------- | ---------- | | Ivan's fish| \= (26 – 8) $\div$ 2 | | | \= 18 $\div$ 2 | | | \= {{{correctAnswer0}}} |

Strategy two (by trial and error): Ivan catches less than half  $\rightarrow$  try 12 If Ivan 12, Mark 20 $\rightarrow$  total = 32 (too high) If Ivan 10, Mark 18 $\rightarrow$  total = 28 (too high) If Ivan 9, Mark 17 $\rightarrow$  total = 26 (correct)
correctAnswer0
9
prefix0
suffix0
fish

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
correctAnswer09

fish

Variant 2

DifficultyLevel

644

Question

Altogether, Natasha and Shirley scored 34 points in a basketball game.

Natasha scored 10 more points than Shirley.

How many points did Shirley score?

Worked Solution

Strategy one:
Shirley’s points = (34 – 10) ÷\div 2
= 24 ÷\div 2
= 12

Strategy two (by trial and error):

Shirley scores less than half the total points  →\rightarrow  try 9

If Shirley 9, Natasha 19 →\rightarrow  total = 28 (too low)

If Shirley 11, Natasha 21 →\rightarrow  total = 32 (too low)

If Shirley 12, Natasha 22 →\rightarrow  total = 34 (correct)

Question Type

Answer Box

Variables

Variable nameVariable value
question
Altogether, Natasha and Shirley scored 34 points in a basketball game. Natasha scored 10 more points than Shirley. How many points did Shirley score?
workedSolution
sm_nogap Strategy one:
| | | | ------------- | ---------- | | Shirley’s points| \= (34 – 10) $\div$ 2 | | | \= 24 $\div$ 2 | | | \= {{{correctAnswer0}}} |

Strategy two (by trial and error): Shirley scores less than half the total points  $\rightarrow$  try 9 If Shirley 9, Natasha 19 $\rightarrow$  total = 28 (too low) If Shirley 11, Natasha 21 $\rightarrow$  total = 32 (too low) If Shirley 12, Natasha 22 $\rightarrow$  total = 34 (correct)
correctAnswer0
12
prefix0
suffix0
points

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

points

Variant 3

DifficultyLevel

650

Question

Altogether, Biggsy and Smacka had saved $67 for a skateboard.

Biggsy has saved $9 more than Smacka.

How much has Smacka saved?

Worked Solution

Strategy one:
Smacka savings = (67 – 9) ÷\div 2
= 58 ÷\div 2
= $29

Strategy two (by trial and error):

Smacka has saved less than half the total  →\rightarrow  try 32

If Smacka 32, Biggsy 41 →\rightarrow  total = 73 (too high)

If Smacka 30, Biggsy 39 →\rightarrow  total = 69 (too high)

If Smacka 29, Biggsy 38 →\rightarrow  total = 67 (correct)

Question Type

Answer Box

Variables

Variable nameVariable value
question
Altogether, Biggsy and Smacka had saved $67 for a skateboard. Biggsy has saved $9 more than Smacka. How much has Smacka saved?
workedSolution
sm_nogap Strategy one:
| | | | ------------- | ---------- | | Smacka savings| \= (67 – 9) $\div$ 2 | | | \= 58 $\div$ 2 | | | \= {{{prefix0}}}{{{correctAnswer0}}} |

Strategy two (by trial and error): Smacka has saved less than half the total  $\rightarrow$  try 32 If Smacka 32, Biggsy 41 $\rightarrow$  total = 73 (too high) If Smacka 30, Biggsy 39 $\rightarrow$  total = 69 (too high) If Smacka 29, Biggsy 38 $\rightarrow$  total = 67 (correct)
correctAnswer0
29
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
correctAnswer029

$

Variant 4

DifficultyLevel

651

Question

Crystal and Shandy bought a total of 71 Merino sheep at the auction.

Crystal bought 13 more sheep than Shandy.

How many sheep did Shandy buy?

Worked Solution

Strategy one:
Shandy's sheep = (71 – 13) ÷\div 2
= 58 ÷\div 2
= 29

Strategy two (by trial and error):

Shandy purchased less than half the total sheep  →\rightarrow  try 34

If Shandy 34, Crystal 47 →\rightarrow  total = 81 (too high)

If Shandy 30, Crystal 43 →\rightarrow  total = 73 (too high)

If Shandy 29, Crystal 42 →\rightarrow  total = 71 (correct)

Question Type

Answer Box

Variables

Variable nameVariable value
question
Crystal and Shandy bought a total of 71 Merino sheep at the auction. Crystal bought 13 more sheep than Shandy. How many sheep did Shandy buy?
workedSolution
sm_nogap Strategy one:
| | | | ------------- | ---------- | | Shandy's sheep| \= (71 – 13) $\div$ 2 | | | \= 58 $\div$ 2 | | | \= {{{correctAnswer0}}} |

Strategy two (by trial and error): Shandy purchased less than half the total sheep  $\rightarrow$  try 34 If Shandy 34, Crystal 47 $\rightarrow$  total = 81 (too high) If Shandy 30, Crystal 43 $\rightarrow$  total = 73 (too high) If Shandy 29, Crystal 42 $\rightarrow$  total = 71 (correct)
correctAnswer0
29
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
correctAnswer029

Tags