Scroll:Heuristics >> Grouping Method >> ps (2449)

Written Instructions:

For each Multiple Choice Question (MCQ), four options are given. One of them is the correct answer. Make your choice (1,2,3 or 4). Write your answers in the brackets provided..

For each Short Answer Question(SAQ) and Long Answer Question(LAQ), write your answers in the blanks provided.

Leave your answers in the simplest form or correct to two decimal places.


 

1)  

At a party, every girl is given 3 packets of chocolates and every boy is given 9 packets of chocolates. There are 4 times as many girls as boys who were at the party.

Given that a total of 483 packets of chocolates were given out, how many girls were at the party 


Answer:_______________




2)  

An angelfish costs $12. A goldfish costs $6 less than an angelfish. Selvan paid $672 for some angelfish and goldfish. He brought 5 times as many as goldfish as angelfish. 

How much more money did he spend on goldfish than on angelfish

$ ___


Answer:_______________




3)  

At a funfair, every child is given 6 mini cupcakes and every adult is given 8 mini cupcakes. There are twice as many children as adults who were at the funfair.

Given that a total of 500 mini cupcakes were given out, how many children were at the funfair 


Answer:_______________




4)  

At a school funfair, every girl is given 5 packets of sweets and every boy is given 11 packets of sweets. There are thrice as many girls as boys who were at the funfair.

Given that a total of 494 packets of sweets were given out, how many girls were at the funfair 


Answer:_______________




5)  

At a party, every girl is given 5 packets of chocolates and every boy is given 6 packets of chocolates. There are 4 times as many girls as boys who were at the party.

Given that a total of 520 packets of chocolates were given out, how many girls were at the party 


Answer:_______________




6)  

An angelfish costs $19. A goldfish costs $6 less than an angelfish. Sriram paid $504 for some angelfish and goldfish. He brought 5 times as many as goldfish as angelfish. 

How much more money did he spend on goldfish than on angelfish

$ ___


Answer:_______________




7)  

At a funfair, every child is given 5 mini cupcakes and every adult is given 11 mini cupcakes. There are twice as many children as adults who were at the funfair.

Given that a total of 693 mini cupcakes were given out, how many children were at the funfair 


Answer:_______________




8)  

At a school funfair, every girl is given 4 packets of sweets and every boy is given 11 packets of sweets. There are thrice as many girls as boys who were at the funfair.

Given that a total of 966 packets of sweets were given out, how many girls were at the funfair 


Answer:_______________




9)  

At a party, every girl is given 4 packets of chocolates and every boy is given 7 packets of chocolates. There are 4 times as many girls as boys who were at the party.

Given that a total of 621 packets of chocolates were given out, how many girls were at the party 


Answer:_______________




10)  

An angelfish costs $14. A goldfish costs $5 less than an angelfish. Kalai paid $531 for some angelfish and goldfish. He brought 5 times as many as goldfish as angelfish. 

How much more money did he spend on goldfish than on angelfish

$ ___


Answer:_______________




 

1)  

At a party, every girl is given 3 packets of chocolates and every boy is given 9 packets of chocolates. There are 4 times as many girls as boys who were at the party.

Given that a total of 483 packets of chocolates were given out, how many girls were at the party 

Answer: 92


SOLUTION 1 :

 Grouping Method



                  3             3             3              3  
483
                 9  

Step 1: 3 + 3  + 3 ï»¿ + 3 + 9 = 21 (1 set)


Step 2: 483 ÷ 21 = 23 sets


             23 sets of 21 packets of chocolates.


             In each set, there are 12 packets of chocolates for girls.


Step 3: 23 x 12 = 276


Step 4: 276 ÷ 3 = 92 (girls)


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Girls 4 units x  3  12 units
Boys 1 unit x  9 9 units
Total        21 units

 

Step 1: 21 units = 483

             1 unit = 483 ÷ 21

                       = 23 sets

Step 2: 4 units = 4 x 23

                        = 92 (girls)



2)  

An angelfish costs $12. A goldfish costs $6 less than an angelfish. Selvan paid $672 for some angelfish and goldfish. He brought 5 times as many as goldfish as angelfish. 

How much more money did he spend on goldfish than on angelfish

Answer: $288


SOLUTION 1 :

 Grouping Method

                     $12  
$672
                        $6         $6         $6         $6      $6  

 

Step 1: $12 - $6 = $6 (goldfish)

Step 2: $6 + $6 + $6 + $6 + $6 + $12 = $42 (1 set)

Step 3: $672 ÷ $42 = 16 sets

              16 sets of $42 for fishes. 

              In each set, there are $30 for goldfishes.

Step 4: 16 x $30 = $480 (goldfish)

Step 5: 16 x $12 = $192 (angelfish)

Step 6: $480 - $192 = $288


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Goldfish 5 units x $6  30 units
Angelfish 1 unit x  $12 12 units 
Total        42 units

 

Step 1: 42 units = $672

             1 unit = $672 ÷ 42

                       = 16 sets

Step 2: 5 units = 5 x 16

                        = 80 

Step 3: 80 x $6 = $480 (goldfish)

Step 4: 16 x $12 = $192 (angelfish)

Step 5: $480 - $192 = $288



3)  

At a funfair, every child is given 6 mini cupcakes and every adult is given 8 mini cupcakes. There are twice as many children as adults who were at the funfair.

Given that a total of 500 mini cupcakes were given out, how many children were at the funfair 

Answer: 50


SOLUTION 1 :

 Grouping Method



                  6             6       
500
                  8  

Step 1: 6 + 6 + 8 = 20 (1 set)


Step 2: 500 ÷ 20 = 25 sets


             25 sets of 20 mini cupcakes.


             In each set, there are 12 mini cupcakes for children.


Step 3: 25 x 12 = 300


Step 4: 300 ÷ 6 = 50 (children)


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Children 2 units x  6  12 units
Adults 1 unit x  8 8 units
Total        20 units

 

Step 1: 20 units = 500

             1 unit = 500 ÷ 20

                       = 25 sets

Step 2: 2 units = 2 x 25

                        = 50 (children)



4)  

At a school funfair, every girl is given 5 packets of sweets and every boy is given 11 packets of sweets. There are thrice as many girls as boys who were at the funfair.

Given that a total of 494 packets of sweets were given out, how many girls were at the funfair 

Answer: 57


SOLUTION 1 :

 Grouping Method

               5             5           5  
494
             11  

Step 1: 5 + 5 + 5 + 11 = 26 (1 set)

Step 2: 494 ÷ 26 = 19 sets

             19 sets of 26 packets of sweets.

             In each set, there are 15 packets of sweets for girls.

Step 3: 19 x 15 = 285

Step 4: 285 ÷ 5 = 57 (girls)


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Girls 3 units x  5  15 units
Boys 1 unit x  11 11 units
Total        26 units

 

Step 1: 26 units = 494

             1 unit = 494 ÷ 26

                       = 19 sets

Step 2: 3 units = 3 x 19

                        = 57 (girls)



5)  

At a party, every girl is given 5 packets of chocolates and every boy is given 6 packets of chocolates. There are 4 times as many girls as boys who were at the party.

Given that a total of 520 packets of chocolates were given out, how many girls were at the party 

Answer: 80


SOLUTION 1 :

 Grouping Method



                  5             5             5              5  
520
                 6  

Step 1: 5 + 5  + 5 ï»¿ + 5 + 6 = 26 (1 set)


Step 2: 520 ÷ 26 = 20 sets


             20 sets of 26 packets of chocolates.


             In each set, there are 20 packets of chocolates for girls.


Step 3: 20 x 20 = 400


Step 4: 400 ÷ 5 = 80 (girls)


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Girls 4 units x  5  20 units
Boys 1 unit x  6 6 units
Total        26 units

 

Step 1: 26 units = 520

             1 unit = 520 ÷ 26

                       = 20 sets

Step 2: 4 units = 4 x 20

                        = 80 (girls)



6)  

An angelfish costs $19. A goldfish costs $6 less than an angelfish. Sriram paid $504 for some angelfish and goldfish. He brought 5 times as many as goldfish as angelfish. 

How much more money did he spend on goldfish than on angelfish

Answer: $276


SOLUTION 1 :

 Grouping Method

                     $19  
$504
                        $13         $13         $13         $13      $13  

 

Step 1: $19 - $6 = $13 (goldfish)

Step 2: $13 + $13 + $13 + $13 + $13 + $19 = $84 (1 set)

Step 3: $504 ÷ $84 = 6 sets

              6 sets of $84 for fishes. 

              In each set, there are $65 for goldfishes.

Step 4: 6 x $65 = $390 (goldfish)

Step 5: 6 x $19 = $114 (angelfish)

Step 6: $390 - $114 = $276


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Goldfish 5 units x $13  65 units
Angelfish 1 unit x  $19 19 units 
Total        84 units

 

Step 1: 84 units = $504

             1 unit = $504 ÷ 84

                       = 6 sets

Step 2: 5 units = 5 x 6

                        = 30 

Step 3: 30 x $13 = $390 (goldfish)

Step 4: 6 x $19 = $114 (angelfish)

Step 5: $390 - $114 = $276



7)  

At a funfair, every child is given 5 mini cupcakes and every adult is given 11 mini cupcakes. There are twice as many children as adults who were at the funfair.

Given that a total of 693 mini cupcakes were given out, how many children were at the funfair 

Answer: 66


SOLUTION 1 :

 Grouping Method



                  5             5       
693
                  11  

Step 1: 5 + 5 + 11 = 21 (1 set)


Step 2: 693 ÷ 21 = 33 sets


             33 sets of 21 mini cupcakes.


             In each set, there are 10 mini cupcakes for children.


Step 3: 33 x 10 = 330


Step 4: 330 ÷ 5 = 66 (children)


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Children 2 units x  5  10 units
Adults 1 unit x  11 11 units
Total        21 units

 

Step 1: 21 units = 693

             1 unit = 693 ÷ 21

                       = 33 sets

Step 2: 2 units = 2 x 33

                        = 66 (children)



8)  

At a school funfair, every girl is given 4 packets of sweets and every boy is given 11 packets of sweets. There are thrice as many girls as boys who were at the funfair.

Given that a total of 966 packets of sweets were given out, how many girls were at the funfair 

Answer: 126


SOLUTION 1 :

 Grouping Method

               4             4           4  
966
             11  

Step 1: 4 + 4 + 4 + 11 = 23 (1 set)

Step 2: 966 ÷ 23 = 42 sets

             42 sets of 23 packets of sweets.

             In each set, there are 12 packets of sweets for girls.

Step 3: 42 x 12 = 504

Step 4: 504 ÷ 4 = 126 (girls)


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Girls 3 units x  4  12 units
Boys 1 unit x  11 11 units
Total        23 units

 

Step 1: 23 units = 966

             1 unit = 966 ÷ 23

                       = 42 sets

Step 2: 3 units = 3 x 42

                        = 126 (girls)



9)  

At a party, every girl is given 4 packets of chocolates and every boy is given 7 packets of chocolates. There are 4 times as many girls as boys who were at the party.

Given that a total of 621 packets of chocolates were given out, how many girls were at the party 

Answer: 108


SOLUTION 1 :

 Grouping Method



                  4             4             4              4  
621
                 7  

Step 1: 4 + 4  + 4 ï»¿ + 4 + 7 = 23 (1 set)


Step 2: 621 ÷ 23 = 27 sets


             27 sets of 23 packets of chocolates.


             In each set, there are 16 packets of chocolates for girls.


Step 3: 27 x 16 = 432


Step 4: 432 ÷ 4 = 108 (girls)


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Girls 4 units x  4  16 units
Boys 1 unit x  7 7 units
Total        23 units

 

Step 1: 23 units = 621

             1 unit = 621 ÷ 23

                       = 27 sets

Step 2: 4 units = 4 x 27

                        = 108 (girls)



10)  

An angelfish costs $14. A goldfish costs $5 less than an angelfish. Kalai paid $531 for some angelfish and goldfish. He brought 5 times as many as goldfish as angelfish. 

How much more money did he spend on goldfish than on angelfish

Answer: $279


SOLUTION 1 :

 Grouping Method

                     $14  
$531
                        $9         $9         $9         $9      $9  

 

Step 1: $14 - $5 = $9 (goldfish)

Step 2: $9 + $9 + $9 + $9 + $9 + $14 = $59 (1 set)

Step 3: $531 ÷ $59 = 9 sets

              9 sets of $59 for fishes. 

              In each set, there are $45 for goldfishes.

Step 4: 9 x $45 = $405 (goldfish)

Step 5: 9 x $14 = $126 (angelfish)

Step 6: $405 - $126 = $279


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Goldfish 5 units x $9  45 units
Angelfish 1 unit x  $14 14 units 
Total        59 units

 

Step 1: 59 units = $531

             1 unit = $531 ÷ 59

                       = 9 sets

Step 2: 5 units = 5 x 9

                        = 45 

Step 3: 45 x $9 = $405 (goldfish)

Step 4: 9 x $14 = $126 (angelfish)

Step 5: $405 - $126 = $279