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 2 packets of chocolates and every boy is given 8 packets of chocolates. There are 4 times as many girls as boys who were at the party.

Given that a total of 496 packets of chocolates were given out, how many girls were at the party 


Answer:_______________




2)  

At a funfair, every child is given 2 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 420 mini cupcakes were given out, how many children were at the funfair 


Answer:_______________




3)  

An angelfish costs $9. A goldfish costs $6 less than an angelfish. Sriram 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:_______________




4)  

At a school funfair, every girl is given 2 packets of sweets and every boy is given 6 packets of sweets. There are thrice as many girls as boys who were at the funfair.

Given that a total of 948 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 8 packets of chocolates. There are 4 times as many girls as boys who were at the party.

Given that a total of 784 packets of chocolates were given out, how many girls were at the party 


Answer:_______________




6)  

At a funfair, every child is given 6 mini cupcakes and every adult is given 9 mini cupcakes. There are twice as many children as adults who were at the funfair.

Given that a total of 609 mini cupcakes were given out, how many children were at the funfair 


Answer:_______________




7)  

An angelfish costs $20. A goldfish costs $6 less than an angelfish. Sriram paid $270 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:_______________




8)  

At a school funfair, every girl is given 4 packets of sweets and every boy is given 12 packets of sweets. There are thrice as many girls as boys who were at the funfair.

Given that a total of 576 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 10 packets of chocolates. There are 4 times as many girls as boys who were at the party.

Given that a total of 650 packets of chocolates were given out, how many girls were at the party 


Answer:_______________




10)  

At a funfair, every child is given 3 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 255 mini cupcakes were given out, how many children were at the funfair 


Answer:_______________




 

1)  

At a party, every girl is given 2 packets of chocolates and every boy is given 8 packets of chocolates. There are 4 times as many girls as boys who were at the party.

Given that a total of 496 packets of chocolates were given out, how many girls were at the party 

Answer: 124


SOLUTION 1 :

 Grouping Method



                  2             2             2              2  
496
                 8  

Step 1: 2 + 2  + 2 ï»¿ + 2 + 8 = 16 (1 set)


Step 2: 496 ÷ 16 = 31 sets


             31 sets of 16 packets of chocolates.


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


Step 3: 31 x 8 = 248


Step 4: 248 ÷ 2 = 124 (girls)


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Girls 4 units x  2  8 units
Boys 1 unit x  8 8 units
Total        16 units

 

Step 1: 16 units = 496

             1 unit = 496 ÷ 16

                       = 31 sets

Step 2: 4 units = 4 x 31

                        = 124 (girls)



2)  

At a funfair, every child is given 2 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 420 mini cupcakes were given out, how many children were at the funfair 

Answer: 56


SOLUTION 1 :

 Grouping Method



                  2             2       
420
                  11  

Step 1: 2 + 2 + 11 = 15 (1 set)


Step 2: 420 ÷ 15 = 28 sets


             28 sets of 15 mini cupcakes.


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


Step 3: 28 x 4 = 112


Step 4: 112 ÷ 2 = 56 (children)


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Children 2 units x  2  4 units
Adults 1 unit x  11 11 units
Total        15 units

 

Step 1: 15 units = 420

             1 unit = 420 ÷ 15

                       = 28 sets

Step 2: 2 units = 2 x 28

                        = 56 (children)



3)  

An angelfish costs $9. A goldfish costs $6 less than an angelfish. Sriram 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: $168


SOLUTION 1 :

 Grouping Method

                     $9  
$672
                        $3         $3         $3         $3      $3  

 

Step 1: $9 - $6 = $3 (goldfish)

Step 2: $3 + $3 + $3 + $3 + $3 + $9 = $24 (1 set)

Step 3: $672 ÷ $24 = 28 sets

              28 sets of $24 for fishes. 

              In each set, there are $15 for goldfishes.

Step 4: 28 x $15 = $420 (goldfish)

Step 5: 28 x $9 = $252 (angelfish)

Step 6: $420 - $252 = $168


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Goldfish 5 units x $3  15 units
Angelfish 1 unit x  $9 9 units 
Total        24 units

 

Step 1: 24 units = $672

             1 unit = $672 ÷ 24

                       = 28 sets

Step 2: 5 units = 5 x 28

                        = 140 

Step 3: 140 x $3 = $420 (goldfish)

Step 4: 28 x $9 = $252 (angelfish)

Step 5: $420 - $252 = $168



4)  

At a school funfair, every girl is given 2 packets of sweets and every boy is given 6 packets of sweets. There are thrice as many girls as boys who were at the funfair.

Given that a total of 948 packets of sweets were given out, how many girls were at the funfair 

Answer: 237


SOLUTION 1 :

 Grouping Method

               2             2           2  
948
             6  

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

Step 2: 948 ÷ 12 = 79 sets

             79 sets of 12 packets of sweets.

             In each set, there are 6 packets of sweets for girls.

Step 3: 79 x 6 = 474

Step 4: 474 ÷ 2 = 237 (girls)


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Girls 3 units x  2  6 units
Boys 1 unit x  6 6 units
Total        12 units

 

Step 1: 12 units = 948

             1 unit = 948 ÷ 12

                       = 79 sets

Step 2: 3 units = 3 x 79

                        = 237 (girls)



5)  

At a party, every girl is given 5 packets of chocolates and every boy is given 8 packets of chocolates. There are 4 times as many girls as boys who were at the party.

Given that a total of 784 packets of chocolates were given out, how many girls were at the party 

Answer: 112


SOLUTION 1 :

 Grouping Method



                  5             5             5              5  
784
                 8  

Step 1: 5 + 5  + 5 ï»¿ + 5 + 8 = 28 (1 set)


Step 2: 784 ÷ 28 = 28 sets


             28 sets of 28 packets of chocolates.


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


Step 3: 28 x 20 = 560


Step 4: 560 ÷ 5 = 112 (girls)


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Girls 4 units x  5  20 units
Boys 1 unit x  8 8 units
Total        28 units

 

Step 1: 28 units = 784

             1 unit = 784 ÷ 28

                       = 28 sets

Step 2: 4 units = 4 x 28

                        = 112 (girls)



6)  

At a funfair, every child is given 6 mini cupcakes and every adult is given 9 mini cupcakes. There are twice as many children as adults who were at the funfair.

Given that a total of 609 mini cupcakes were given out, how many children were at the funfair 

Answer: 58


SOLUTION 1 :

 Grouping Method



                  6             6       
609
                  9  

Step 1: 6 + 6 + 9 = 21 (1 set)


Step 2: 609 ÷ 21 = 29 sets


             29 sets of 21 mini cupcakes.


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


Step 3: 29 x 12 = 348


Step 4: 348 ÷ 6 = 58 (children)


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Children 2 units x  6  12 units
Adults 1 unit x  9 9 units
Total        21 units

 

Step 1: 21 units = 609

             1 unit = 609 ÷ 21

                       = 29 sets

Step 2: 2 units = 2 x 29

                        = 58 (children)



7)  

An angelfish costs $20. A goldfish costs $6 less than an angelfish. Sriram paid $270 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: $150


SOLUTION 1 :

 Grouping Method

                     $20  
$270
                        $14         $14         $14         $14      $14  

 

Step 1: $20 - $6 = $14 (goldfish)

Step 2: $14 + $14 + $14 + $14 + $14 + $20 = $90 (1 set)

Step 3: $270 ÷ $90 = 3 sets

              3 sets of $90 for fishes. 

              In each set, there are $70 for goldfishes.

Step 4: 3 x $70 = $210 (goldfish)

Step 5: 3 x $20 = $60 (angelfish)

Step 6: $210 - $60 = $150


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Goldfish 5 units x $14  70 units
Angelfish 1 unit x  $20 20 units 
Total        90 units

 

Step 1: 90 units = $270

             1 unit = $270 ÷ 90

                       = 3 sets

Step 2: 5 units = 5 x 3

                        = 15 

Step 3: 15 x $14 = $210 (goldfish)

Step 4: 3 x $20 = $60 (angelfish)

Step 5: $210 - $60 = $150



8)  

At a school funfair, every girl is given 4 packets of sweets and every boy is given 12 packets of sweets. There are thrice as many girls as boys who were at the funfair.

Given that a total of 576 packets of sweets were given out, how many girls were at the funfair 

Answer: 72


SOLUTION 1 :

 Grouping Method

               4             4           4  
576
             12  

Step 1: 4 + 4 + 4 + 12 = 24 (1 set)

Step 2: 576 ÷ 24 = 24 sets

             24 sets of 24 packets of sweets.

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

Step 3: 24 x 12 = 288

Step 4: 288 ÷ 4 = 72 (girls)


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Girls 3 units x  4  12 units
Boys 1 unit x  12 12 units
Total        24 units

 

Step 1: 24 units = 576

             1 unit = 576 ÷ 24

                       = 24 sets

Step 2: 3 units = 3 x 24

                        = 72 (girls)



9)  

At a party, every girl is given 4 packets of chocolates and every boy is given 10 packets of chocolates. There are 4 times as many girls as boys who were at the party.

Given that a total of 650 packets of chocolates were given out, how many girls were at the party 

Answer: 100


SOLUTION 1 :

 Grouping Method



                  4             4             4              4  
650
                 10  

Step 1: 4 + 4  + 4 ï»¿ + 4 + 10 = 26 (1 set)


Step 2: 650 ÷ 26 = 25 sets


             25 sets of 26 packets of chocolates.


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


Step 3: 25 x 16 = 400


Step 4: 400 ÷ 4 = 100 (girls)


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Girls 4 units x  4  16 units
Boys 1 unit x  10 10 units
Total        26 units

 

Step 1: 26 units = 650

             1 unit = 650 ÷ 26

                       = 25 sets

Step 2: 4 units = 4 x 25

                        = 100 (girls)



10)  

At a funfair, every child is given 3 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 255 mini cupcakes were given out, how many children were at the funfair 

Answer: 30


SOLUTION 1 :

 Grouping Method



                  3             3       
255
                  11  

Step 1: 3 + 3 + 11 = 17 (1 set)


Step 2: 255 ÷ 17 = 15 sets


             15 sets of 17 mini cupcakes.


             In each set, there are 6 mini cupcakes for children.


Step 3: 15 x 6 = 90


Step 4: 90 ÷ 3 = 30 (children)


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Children 2 units x  3  6 units
Adults 1 unit x  11 11 units
Total        17 units

 

Step 1: 17 units = 255

             1 unit = 255 ÷ 17

                       = 15 sets

Step 2: 2 units = 2 x 15

                        = 30 (children)