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 10 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:_______________




2)  

An angelfish costs $17. A goldfish costs $6 less than an angelfish. Sriram paid $216 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 7 packets of sweets. There are thrice as many girls as boys who were at the funfair.

Given that a total of 440 packets of sweets were given out, how many girls were at the funfair 


Answer:_______________




4)  

At a funfair, every child is given 4 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 352 mini cupcakes were given out, how many children were at the funfair 


Answer:_______________




5)  

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


Answer:_______________




6)  

An angelfish costs $11. A goldfish costs $6 less than an angelfish. Selvan paid $252 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 5 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 374 packets of sweets were given out, how many girls were at the funfair 


Answer:_______________




8)  

At a funfair, every child is given 5 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 527 mini cupcakes were given out, how many children were at the funfair 


Answer:_______________




9)  

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


Answer:_______________




10)  

An angelfish costs $15. A goldfish costs $3 less than an angelfish. Karna paid $600 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 10 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: 56


SOLUTION 1 :

 Grouping Method



                  3             3             3              3  
308
                 10  

Step 1: 3 + 3  + 3 ï»¿ + 3 + 10 = 22 (1 set)


Step 2: 308 ÷ 22 = 14 sets


             14 sets of 22 packets of chocolates.


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


Step 3: 14 x 12 = 168


Step 4: 168 ÷ 3 = 56 (girls)


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Girls 4 units x  3  12 units
Boys 1 unit x  10 10 units
Total        22 units

 

Step 1: 22 units = 308

             1 unit = 308 ÷ 22

                       = 14 sets

Step 2: 4 units = 4 x 14

                        = 56 (girls)



2)  

An angelfish costs $17. A goldfish costs $6 less than an angelfish. Sriram paid $216 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: $114


SOLUTION 1 :

 Grouping Method

                     $17  
$216
                        $11         $11         $11         $11      $11  

 

Step 1: $17 - $6 = $11 (goldfish)

Step 2: $11 + $11 + $11 + $11 + $11 + $17 = $72 (1 set)

Step 3: $216 ÷ $72 = 3 sets

              3 sets of $72 for fishes. 

              In each set, there are $55 for goldfishes.

Step 4: 3 x $55 = $165 (goldfish)

Step 5: 3 x $17 = $51 (angelfish)

Step 6: $165 - $51 = $114


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Goldfish 5 units x $11  55 units
Angelfish 1 unit x  $17 17 units 
Total        72 units

 

Step 1: 72 units = $216

             1 unit = $216 ÷ 72

                       = 3 sets

Step 2: 5 units = 5 x 3

                        = 15 

Step 3: 15 x $11 = $165 (goldfish)

Step 4: 3 x $17 = $51 (angelfish)

Step 5: $165 - $51 = $114



3)  

At a school funfair, every girl is given 5 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 440 packets of sweets were given out, how many girls were at the funfair 

Answer: 60


SOLUTION 1 :

 Grouping Method

               5             5           5  
440
             7  

Step 1: 5 + 5 + 5 + 7 = 22 (1 set)

Step 2: 440 ÷ 22 = 20 sets

             20 sets of 22 packets of sweets.

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

Step 3: 20 x 15 = 300

Step 4: 300 ÷ 5 = 60 (girls)


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Girls 3 units x  5  15 units
Boys 1 unit x  7 7 units
Total        22 units

 

Step 1: 22 units = 440

             1 unit = 440 ÷ 22

                       = 20 sets

Step 2: 3 units = 3 x 20

                        = 60 (girls)



4)  

At a funfair, every child is given 4 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 352 mini cupcakes were given out, how many children were at the funfair 

Answer: 44


SOLUTION 1 :

 Grouping Method



                  4             4       
352
                  8  

Step 1: 4 + 4 + 8 = 16 (1 set)


Step 2: 352 ÷ 16 = 22 sets


             22 sets of 16 mini cupcakes.


             In each set, there are 8 mini cupcakes for children.


Step 3: 22 x 8 = 176


Step 4: 176 ÷ 4 = 44 (children)


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Children 2 units x  4  8 units
Adults 1 unit x  8 8 units
Total        16 units

 

Step 1: 16 units = 352

             1 unit = 352 ÷ 16

                       = 22 sets

Step 2: 2 units = 2 x 22

                        = 44 (children)



5)  

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

Answer: 60


SOLUTION 1 :

 Grouping Method



                  4             4             4              4  
345
                 7  

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


Step 2: 345 ÷ 23 = 15 sets


             15 sets of 23 packets of chocolates.


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


Step 3: 15 x 16 = 240


Step 4: 240 ÷ 4 = 60 (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 = 345

             1 unit = 345 ÷ 23

                       = 15 sets

Step 2: 4 units = 4 x 15

                        = 60 (girls)



6)  

An angelfish costs $11. A goldfish costs $6 less than an angelfish. Selvan paid $252 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: $98


SOLUTION 1 :

 Grouping Method

                     $11  
$252
                        $5         $5         $5         $5      $5  

 

Step 1: $11 - $6 = $5 (goldfish)

Step 2: $5 + $5 + $5 + $5 + $5 + $11 = $36 (1 set)

Step 3: $252 ÷ $36 = 7 sets

              7 sets of $36 for fishes. 

              In each set, there are $25 for goldfishes.

Step 4: 7 x $25 = $175 (goldfish)

Step 5: 7 x $11 = $77 (angelfish)

Step 6: $175 - $77 = $98


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Goldfish 5 units x $5  25 units
Angelfish 1 unit x  $11 11 units 
Total        36 units

 

Step 1: 36 units = $252

             1 unit = $252 ÷ 36

                       = 7 sets

Step 2: 5 units = 5 x 7

                        = 35 

Step 3: 35 x $5 = $175 (goldfish)

Step 4: 7 x $11 = $77 (angelfish)

Step 5: $175 - $77 = $98



7)  

At a school funfair, every girl is given 5 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 374 packets of sweets were given out, how many girls were at the funfair 

Answer: 51


SOLUTION 1 :

 Grouping Method

               5             5           5  
374
             7  

Step 1: 5 + 5 + 5 + 7 = 22 (1 set)

Step 2: 374 ÷ 22 = 17 sets

             17 sets of 22 packets of sweets.

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

Step 3: 17 x 15 = 255

Step 4: 255 ÷ 5 = 51 (girls)


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Girls 3 units x  5  15 units
Boys 1 unit x  7 7 units
Total        22 units

 

Step 1: 22 units = 374

             1 unit = 374 ÷ 22

                       = 17 sets

Step 2: 3 units = 3 x 17

                        = 51 (girls)



8)  

At a funfair, every child is given 5 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 527 mini cupcakes were given out, how many children were at the funfair 

Answer: 62


SOLUTION 1 :

 Grouping Method



                  5             5       
527
                  7  

Step 1: 5 + 5 + 7 = 17 (1 set)


Step 2: 527 ÷ 17 = 31 sets


             31 sets of 17 mini cupcakes.


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


Step 3: 31 x 10 = 310


Step 4: 310 ÷ 5 = 62 (children)


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Children 2 units x  5  10 units
Adults 1 unit x  7 7 units
Total        17 units

 

Step 1: 17 units = 527

             1 unit = 527 ÷ 17

                       = 31 sets

Step 2: 2 units = 2 x 31

                        = 62 (children)



9)  

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

Answer: 88


SOLUTION 1 :

 Grouping Method



                  5             5             5              5  
616
                 8  

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


Step 2: 616 ÷ 28 = 22 sets


             22 sets of 28 packets of chocolates.


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


Step 3: 22 x 20 = 440


Step 4: 440 ÷ 5 = 88 (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 = 616

             1 unit = 616 ÷ 28

                       = 22 sets

Step 2: 4 units = 4 x 22

                        = 88 (girls)



10)  

An angelfish costs $15. A goldfish costs $3 less than an angelfish. Karna paid $600 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: $360


SOLUTION 1 :

 Grouping Method

                     $15  
$600
                        $12         $12         $12         $12      $12  

 

Step 1: $15 - $3 = $12 (goldfish)

Step 2: $12 + $12 + $12 + $12 + $12 + $15 = $75 (1 set)

Step 3: $600 ÷ $75 = 8 sets

              8 sets of $75 for fishes. 

              In each set, there are $60 for goldfishes.

Step 4: 8 x $60 = $480 (goldfish)

Step 5: 8 x $15 = $120 (angelfish)

Step 6: $480 - $120 = $360


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Goldfish 5 units x $12  60 units
Angelfish 1 unit x  $15 15 units 
Total        75 units

 

Step 1: 75 units = $600

             1 unit = $600 ÷ 75

                       = 8 sets

Step 2: 5 units = 5 x 8

                        = 40 

Step 3: 40 x $12 = $480 (goldfish)

Step 4: 8 x $15 = $120 (angelfish)

Step 5: $480 - $120 = $360