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 5 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 783 packets of chocolates were given out, how many girls were at the party 


Answer:_______________




2)  

An angelfish costs $14. A goldfish costs $3 less than an angelfish. Kalai paid $414 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 2 mini cupcakes and every adult is given 7 mini cupcakes. There are twice as many children as adults who were at the funfair.

Given that a total of 616 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 10 packets of sweets. There are thrice as many girls as boys who were at the funfair.

Given that a total of 600 packets of sweets were given out, how many girls were at the funfair 


Answer:_______________




5)  

At a party, every girl is given 3 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 216 packets of chocolates were given out, how many girls were at the party 


Answer:_______________




6)  

An angelfish costs $11. A goldfish costs $3 less than an angelfish. Prem paid $459 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 2 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 221 mini cupcakes were given out, how many children were at the funfair 


Answer:_______________




8)  

At a school funfair, every girl is given 3 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 620 packets of sweets were given out, how many girls were at the funfair 


Answer:_______________




9)  

At a party, every girl is given 2 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 221 packets of chocolates were given out, how many girls were at the party 


Answer:_______________




10)  

An angelfish costs $11. A goldfish costs $4 less than an angelfish. Balaji paid $644 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 5 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 783 packets of chocolates were given out, how many girls were at the party 

Answer: 108


SOLUTION 1 :

 Grouping Method



                  5             5             5              5  
783
                 9  

Step 1: 5 + 5  + 5 ï»¿ + 5 + 9 = 29 (1 set)


Step 2: 783 ÷ 29 = 27 sets


             27 sets of 29 packets of chocolates.


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


Step 3: 27 x 20 = 540


Step 4: 540 ÷ 5 = 108 (girls)


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Girls 4 units x  5  20 units
Boys 1 unit x  9 9 units
Total        29 units

 

Step 1: 29 units = 783

             1 unit = 783 ÷ 29

                       = 27 sets

Step 2: 4 units = 4 x 27

                        = 108 (girls)



2)  

An angelfish costs $14. A goldfish costs $3 less than an angelfish. Kalai paid $414 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: $246


SOLUTION 1 :

 Grouping Method

                     $14  
$414
                        $11         $11         $11         $11      $11  

 

Step 1: $14 - $3 = $11 (goldfish)

Step 2: $11 + $11 + $11 + $11 + $11 + $14 = $69 (1 set)

Step 3: $414 ÷ $69 = 6 sets

              6 sets of $69 for fishes. 

              In each set, there are $55 for goldfishes.

Step 4: 6 x $55 = $330 (goldfish)

Step 5: 6 x $14 = $84 (angelfish)

Step 6: $330 - $84 = $246


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Goldfish 5 units x $11  55 units
Angelfish 1 unit x  $14 14 units 
Total        69 units

 

Step 1: 69 units = $414

             1 unit = $414 ÷ 69

                       = 6 sets

Step 2: 5 units = 5 x 6

                        = 30 

Step 3: 30 x $11 = $330 (goldfish)

Step 4: 6 x $14 = $84 (angelfish)

Step 5: $330 - $84 = $246



3)  

At a funfair, every child is given 2 mini cupcakes and every adult is given 7 mini cupcakes. There are twice as many children as adults who were at the funfair.

Given that a total of 616 mini cupcakes were given out, how many children were at the funfair 

Answer: 112


SOLUTION 1 :

 Grouping Method



                  2             2       
616
                  7  

Step 1: 2 + 2 + 7 = 11 (1 set)


Step 2: 616 ÷ 11 = 56 sets


             56 sets of 11 mini cupcakes.


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


Step 3: 56 x 4 = 224


Step 4: 224 ÷ 2 = 112 (children)


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Children 2 units x  2  4 units
Adults 1 unit x  7 7 units
Total        11 units

 

Step 1: 11 units = 616

             1 unit = 616 ÷ 11

                       = 56 sets

Step 2: 2 units = 2 x 56

                        = 112 (children)



4)  

At a school funfair, every girl is given 5 packets of sweets and every boy is given 10 packets of sweets. There are thrice as many girls as boys who were at the funfair.

Given that a total of 600 packets of sweets were given out, how many girls were at the funfair 

Answer: 72


SOLUTION 1 :

 Grouping Method

               5             5           5  
600
             10  

Step 1: 5 + 5 + 5 + 10 = 25 (1 set)

Step 2: 600 ÷ 25 = 24 sets

             24 sets of 25 packets of sweets.

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

Step 3: 24 x 15 = 360

Step 4: 360 ÷ 5 = 72 (girls)


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Girls 3 units x  5  15 units
Boys 1 unit x  10 10 units
Total        25 units

 

Step 1: 25 units = 600

             1 unit = 600 ÷ 25

                       = 24 sets

Step 2: 3 units = 3 x 24

                        = 72 (girls)



5)  

At a party, every girl is given 3 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 216 packets of chocolates were given out, how many girls were at the party 

Answer: 48


SOLUTION 1 :

 Grouping Method



                  3             3             3              3  
216
                 6  

Step 1: 3 + 3  + 3 ï»¿ + 3 + 6 = 18 (1 set)


Step 2: 216 ÷ 18 = 12 sets


             12 sets of 18 packets of chocolates.


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


Step 3: 12 x 12 = 144


Step 4: 144 ÷ 3 = 48 (girls)


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Girls 4 units x  3  12 units
Boys 1 unit x  6 6 units
Total        18 units

 

Step 1: 18 units = 216

             1 unit = 216 ÷ 18

                       = 12 sets

Step 2: 4 units = 4 x 12

                        = 48 (girls)



6)  

An angelfish costs $11. A goldfish costs $3 less than an angelfish. Prem paid $459 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: $261


SOLUTION 1 :

 Grouping Method

                     $11  
$459
                        $8         $8         $8         $8      $8  

 

Step 1: $11 - $3 = $8 (goldfish)

Step 2: $8 + $8 + $8 + $8 + $8 + $11 = $51 (1 set)

Step 3: $459 ÷ $51 = 9 sets

              9 sets of $51 for fishes. 

              In each set, there are $40 for goldfishes.

Step 4: 9 x $40 = $360 (goldfish)

Step 5: 9 x $11 = $99 (angelfish)

Step 6: $360 - $99 = $261


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Goldfish 5 units x $8  40 units
Angelfish 1 unit x  $11 11 units 
Total        51 units

 

Step 1: 51 units = $459

             1 unit = $459 ÷ 51

                       = 9 sets

Step 2: 5 units = 5 x 9

                        = 45 

Step 3: 45 x $8 = $360 (goldfish)

Step 4: 9 x $11 = $99 (angelfish)

Step 5: $360 - $99 = $261



7)  

At a funfair, every child is given 2 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 221 mini cupcakes were given out, how many children were at the funfair 

Answer: 34


SOLUTION 1 :

 Grouping Method



                  2             2       
221
                  9  

Step 1: 2 + 2 + 9 = 13 (1 set)


Step 2: 221 ÷ 13 = 17 sets


             17 sets of 13 mini cupcakes.


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


Step 3: 17 x 4 = 68


Step 4: 68 ÷ 2 = 34 (children)


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Children 2 units x  2  4 units
Adults 1 unit x  9 9 units
Total        13 units

 

Step 1: 13 units = 221

             1 unit = 221 ÷ 13

                       = 17 sets

Step 2: 2 units = 2 x 17

                        = 34 (children)



8)  

At a school funfair, every girl is given 3 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 620 packets of sweets were given out, how many girls were at the funfair 

Answer: 93


SOLUTION 1 :

 Grouping Method

               3             3           3  
620
             11  

Step 1: 3 + 3 + 3 + 11 = 20 (1 set)

Step 2: 620 ÷ 20 = 31 sets

             31 sets of 20 packets of sweets.

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

Step 3: 31 x 9 = 279

Step 4: 279 ÷ 3 = 93 (girls)


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Girls 3 units x  3  9 units
Boys 1 unit x  11 11 units
Total        20 units

 

Step 1: 20 units = 620

             1 unit = 620 ÷ 20

                       = 31 sets

Step 2: 3 units = 3 x 31

                        = 93 (girls)



9)  

At a party, every girl is given 2 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 221 packets of chocolates were given out, how many girls were at the party 

Answer: 52


SOLUTION 1 :

 Grouping Method



                  2             2             2              2  
221
                 9  

Step 1: 2 + 2  + 2 ï»¿ + 2 + 9 = 17 (1 set)


Step 2: 221 ÷ 17 = 13 sets


             13 sets of 17 packets of chocolates.


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


Step 3: 13 x 8 = 104


Step 4: 104 ÷ 2 = 52 (girls)


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Girls 4 units x  2  8 units
Boys 1 unit x  9 9 units
Total        17 units

 

Step 1: 17 units = 221

             1 unit = 221 ÷ 17

                       = 13 sets

Step 2: 4 units = 4 x 13

                        = 52 (girls)



10)  

An angelfish costs $11. A goldfish costs $4 less than an angelfish. Balaji paid $644 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: $336


SOLUTION 1 :

 Grouping Method

                     $11  
$644
                        $7         $7         $7         $7      $7  

 

Step 1: $11 - $4 = $7 (goldfish)

Step 2: $7 + $7 + $7 + $7 + $7 + $11 = $46 (1 set)

Step 3: $644 ÷ $46 = 14 sets

              14 sets of $46 for fishes. 

              In each set, there are $35 for goldfishes.

Step 4: 14 x $35 = $490 (goldfish)

Step 5: 14 x $11 = $154 (angelfish)

Step 6: $490 - $154 = $336


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Goldfish 5 units x $7  35 units
Angelfish 1 unit x  $11 11 units 
Total        46 units

 

Step 1: 46 units = $644

             1 unit = $644 ÷ 46

                       = 14 sets

Step 2: 5 units = 5 x 14

                        = 70 

Step 3: 70 x $7 = $490 (goldfish)

Step 4: 14 x $11 = $154 (angelfish)

Step 5: $490 - $154 = $336