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 funfair, every child is given 6 mini cupcakes and every adult is given 10 mini cupcakes. There are twice as many children as adults who were at the funfair.

Given that a total of 836 mini cupcakes were given out, how many children were at the funfair 


Answer:_______________




2)  

An angelfish costs $19. A goldfish costs $4 less than an angelfish. Pugal paid $752 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 school funfair, every girl is given 5 packets of sweets and every boy is given 9 packets of sweets. There are thrice as many girls as boys who were at the funfair.

Given that a total of 648 packets of sweets were given out, how many girls were at the funfair 


Answer:_______________




4)  

At a party, every girl is given 2 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 308 packets of chocolates were given out, how many girls were at the party 


Answer:_______________




5)  

At a funfair, every child is given 2 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 708 mini cupcakes were given out, how many children were at the funfair 


Answer:_______________




6)  

An angelfish costs $15. A goldfish costs $5 less than an angelfish. Moorthi paid $390 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 school funfair, every girl is given 3 packets of sweets and every boy is given 7 packets of sweets. There are thrice as many girls as boys who were at the funfair.

Given that a total of 752 packets of sweets were given out, how many girls were at the funfair 


Answer:_______________




8)  

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 368 packets of chocolates were given out, how many girls were at the party 


Answer:_______________




9)  

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 200 mini cupcakes were given out, how many children were at the funfair 


Answer:_______________




10)  

An angelfish costs $9. A goldfish costs $5 less than an angelfish. Kumar paid $406 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 funfair, every child is given 6 mini cupcakes and every adult is given 10 mini cupcakes. There are twice as many children as adults who were at the funfair.

Given that a total of 836 mini cupcakes were given out, how many children were at the funfair 

Answer: 76


SOLUTION 1 :

 Grouping Method



                  6             6       
836
                  10  

Step 1: 6 + 6 + 10 = 22 (1 set)


Step 2: 836 ÷ 22 = 38 sets


             38 sets of 22 mini cupcakes.


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


Step 3: 38 x 12 = 456


Step 4: 456 ÷ 6 = 76 (children)


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Children 2 units x  6  12 units
Adults 1 unit x  10 10 units
Total        22 units

 

Step 1: 22 units = 836

             1 unit = 836 ÷ 22

                       = 38 sets

Step 2: 2 units = 2 x 38

                        = 76 (children)



2)  

An angelfish costs $19. A goldfish costs $4 less than an angelfish. Pugal paid $752 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: $448


SOLUTION 1 :

 Grouping Method

                     $19  
$752
                        $15         $15         $15         $15      $15  

 

Step 1: $19 - $4 = $15 (goldfish)

Step 2: $15 + $15 + $15 + $15 + $15 + $19 = $94 (1 set)

Step 3: $752 ÷ $94 = 8 sets

              8 sets of $94 for fishes. 

              In each set, there are $75 for goldfishes.

Step 4: 8 x $75 = $600 (goldfish)

Step 5: 8 x $19 = $152 (angelfish)

Step 6: $600 - $152 = $448


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Goldfish 5 units x $15  75 units
Angelfish 1 unit x  $19 19 units 
Total        94 units

 

Step 1: 94 units = $752

             1 unit = $752 ÷ 94

                       = 8 sets

Step 2: 5 units = 5 x 8

                        = 40 

Step 3: 40 x $15 = $600 (goldfish)

Step 4: 8 x $19 = $152 (angelfish)

Step 5: $600 - $152 = $448



3)  

At a school funfair, every girl is given 5 packets of sweets and every boy is given 9 packets of sweets. There are thrice as many girls as boys who were at the funfair.

Given that a total of 648 packets of sweets were given out, how many girls were at the funfair 

Answer: 81


SOLUTION 1 :

 Grouping Method

               5             5           5  
648
             9  

Step 1: 5 + 5 + 5 + 9 = 24 (1 set)

Step 2: 648 ÷ 24 = 27 sets

             27 sets of 24 packets of sweets.

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

Step 3: 27 x 15 = 405

Step 4: 405 ÷ 5 = 81 (girls)


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Girls 3 units x  5  15 units
Boys 1 unit x  9 9 units
Total        24 units

 

Step 1: 24 units = 648

             1 unit = 648 ÷ 24

                       = 27 sets

Step 2: 3 units = 3 x 27

                        = 81 (girls)



4)  

At a party, every girl is given 2 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 308 packets of chocolates were given out, how many girls were at the party 

Answer: 88


SOLUTION 1 :

 Grouping Method



                  2             2             2              2  
308
                 6  

Step 1: 2 + 2  + 2 ï»¿ + 2 + 6 = 14 (1 set)


Step 2: 308 ÷ 14 = 22 sets


             22 sets of 14 packets of chocolates.


             In each set, there are 8 packets of chocolates for girls.


Step 3: 22 x 8 = 176


Step 4: 176 ÷ 2 = 88 (girls)


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Girls 4 units x  2  8 units
Boys 1 unit x  6 6 units
Total        14 units

 

Step 1: 14 units = 308

             1 unit = 308 ÷ 14

                       = 22 sets

Step 2: 4 units = 4 x 22

                        = 88 (girls)



5)  

At a funfair, every child is given 2 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 708 mini cupcakes were given out, how many children were at the funfair 

Answer: 118


SOLUTION 1 :

 Grouping Method



                  2             2       
708
                  8  

Step 1: 2 + 2 + 8 = 12 (1 set)


Step 2: 708 ÷ 12 = 59 sets


             59 sets of 12 mini cupcakes.


             In each set, there are 4 mini cupcakes for children.


Step 3: 59 x 4 = 236


Step 4: 236 ÷ 2 = 118 (children)


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Children 2 units x  2  4 units
Adults 1 unit x  8 8 units
Total        12 units

 

Step 1: 12 units = 708

             1 unit = 708 ÷ 12

                       = 59 sets

Step 2: 2 units = 2 x 59

                        = 118 (children)



6)  

An angelfish costs $15. A goldfish costs $5 less than an angelfish. Moorthi paid $390 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: $210


SOLUTION 1 :

 Grouping Method

                     $15  
$390
                        $10         $10         $10         $10      $10  

 

Step 1: $15 - $5 = $10 (goldfish)

Step 2: $10 + $10 + $10 + $10 + $10 + $15 = $65 (1 set)

Step 3: $390 ÷ $65 = 6 sets

              6 sets of $65 for fishes. 

              In each set, there are $50 for goldfishes.

Step 4: 6 x $50 = $300 (goldfish)

Step 5: 6 x $15 = $90 (angelfish)

Step 6: $300 - $90 = $210


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Goldfish 5 units x $10  50 units
Angelfish 1 unit x  $15 15 units 
Total        65 units

 

Step 1: 65 units = $390

             1 unit = $390 ÷ 65

                       = 6 sets

Step 2: 5 units = 5 x 6

                        = 30 

Step 3: 30 x $10 = $300 (goldfish)

Step 4: 6 x $15 = $90 (angelfish)

Step 5: $300 - $90 = $210



7)  

At a school funfair, every girl is given 3 packets of sweets and every boy is given 7 packets of sweets. There are thrice as many girls as boys who were at the funfair.

Given that a total of 752 packets of sweets were given out, how many girls were at the funfair 

Answer: 141


SOLUTION 1 :

 Grouping Method

               3             3           3  
752
             7  

Step 1: 3 + 3 + 3 + 7 = 16 (1 set)

Step 2: 752 ÷ 16 = 47 sets

             47 sets of 16 packets of sweets.

             In each set, there are 9 packets of sweets for girls.

Step 3: 47 x 9 = 423

Step 4: 423 ÷ 3 = 141 (girls)


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Girls 3 units x  3  9 units
Boys 1 unit x  7 7 units
Total        16 units

 

Step 1: 16 units = 752

             1 unit = 752 ÷ 16

                       = 47 sets

Step 2: 3 units = 3 x 47

                        = 141 (girls)



8)  

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 368 packets of chocolates were given out, how many girls were at the party 

Answer: 64


SOLUTION 1 :

 Grouping Method



                  4             4             4              4  
368
                 7  

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


Step 2: 368 ÷ 23 = 16 sets


             16 sets of 23 packets of chocolates.


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


Step 3: 16 x 16 = 256


Step 4: 256 ÷ 4 = 64 (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 = 368

             1 unit = 368 ÷ 23

                       = 16 sets

Step 2: 4 units = 4 x 16

                        = 64 (girls)



9)  

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 200 mini cupcakes were given out, how many children were at the funfair 

Answer: 20


SOLUTION 1 :

 Grouping Method



                  6             6       
200
                  8  

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


Step 2: 200 ÷ 20 = 10 sets


             10 sets of 20 mini cupcakes.


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


Step 3: 10 x 12 = 120


Step 4: 120 ÷ 6 = 20 (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 = 200

             1 unit = 200 ÷ 20

                       = 10 sets

Step 2: 2 units = 2 x 10

                        = 20 (children)



10)  

An angelfish costs $9. A goldfish costs $5 less than an angelfish. Kumar paid $406 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: $154


SOLUTION 1 :

 Grouping Method

                     $9  
$406
                        $4         $4         $4         $4      $4  

 

Step 1: $9 - $5 = $4 (goldfish)

Step 2: $4 + $4 + $4 + $4 + $4 + $9 = $29 (1 set)

Step 3: $406 ÷ $29 = 14 sets

              14 sets of $29 for fishes. 

              In each set, there are $20 for goldfishes.

Step 4: 14 x $20 = $280 (goldfish)

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

Step 6: $280 - $126 = $154


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Goldfish 5 units x $4  20 units
Angelfish 1 unit x  $9 9 units 
Total        29 units

 

Step 1: 29 units = $406

             1 unit = $406 ÷ 29

                       = 14 sets

Step 2: 5 units = 5 x 14

                        = 70 

Step 3: 70 x $4 = $280 (goldfish)

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

Step 5: $280 - $126 = $154