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)  

An angelfish costs $10. A goldfish costs $5 less than an angelfish. Chidambaram paid $280 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:_______________




2)  

At a school funfair, every girl is given 4 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 374 packets of sweets were given out, how many girls were at the funfair 


Answer:_______________




3)  

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


Answer:_______________




4)  

At a funfair, every child is given 3 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 315 mini cupcakes were given out, how many children were at the funfair 


Answer:_______________




5)  

An angelfish costs $17. A goldfish costs $5 less than an angelfish. Sriram paid $539 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:_______________




6)  

At a school funfair, every girl is given 2 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 432 packets of sweets were given out, how many girls were at the funfair 


Answer:_______________




7)  

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


Answer:_______________




8)  

At a funfair, every child is given 5 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 608 mini cupcakes were given out, how many children were at the funfair 


Answer:_______________




9)  

An angelfish costs $11. A goldfish costs $6 less than an angelfish. Chidambaram paid $396 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:_______________




10)  

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 300 packets of sweets were given out, how many girls were at the funfair 


Answer:_______________




 

1)  

An angelfish costs $10. A goldfish costs $5 less than an angelfish. Chidambaram paid $280 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: $120


SOLUTION 1 :

 Grouping Method

                     $10  
$280
                        $5         $5         $5         $5      $5  

 

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

Step 2: $5 + $5 + $5 + $5 + $5 + $10 = $35 (1 set)

Step 3: $280 ÷ $35 = 8 sets

              8 sets of $35 for fishes. 

              In each set, there are $25 for goldfishes.

Step 4: 8 x $25 = $200 (goldfish)

Step 5: 8 x $10 = $80 (angelfish)

Step 6: $200 - $80 = $120


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Goldfish 5 units x $5  25 units
Angelfish 1 unit x  $10 10 units 
Total        35 units

 

Step 1: 35 units = $280

             1 unit = $280 ÷ 35

                       = 8 sets

Step 2: 5 units = 5 x 8

                        = 40 

Step 3: 40 x $5 = $200 (goldfish)

Step 4: 8 x $10 = $80 (angelfish)

Step 5: $200 - $80 = $120



2)  

At a school funfair, every girl is given 4 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 374 packets of sweets were given out, how many girls were at the funfair 

Answer: 51


SOLUTION 1 :

 Grouping Method

               4             4           4  
374
             10  

Step 1: 4 + 4 + 4 + 10 = 22 (1 set)

Step 2: 374 ÷ 22 = 17 sets

             17 sets of 22 packets of sweets.

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

Step 3: 17 x 12 = 204

Step 4: 204 ÷ 4 = 51 (girls)


SOLUTION 2 :

 Number x Value Method

 

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

 

Step 1: 22 units = 374

             1 unit = 374 ÷ 22

                       = 17 sets

Step 2: 3 units = 3 x 17

                        = 51 (girls)



3)  

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

Answer: 148


SOLUTION 1 :

 Grouping Method



                  3             3             3              3  
777
                 9  

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


Step 2: 777 ÷ 21 = 37 sets


             37 sets of 21 packets of chocolates.


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


Step 3: 37 x 12 = 444


Step 4: 444 ÷ 3 = 148 (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 = 777

             1 unit = 777 ÷ 21

                       = 37 sets

Step 2: 4 units = 4 x 37

                        = 148 (girls)



4)  

At a funfair, every child is given 3 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 315 mini cupcakes were given out, how many children were at the funfair 

Answer: 42


SOLUTION 1 :

 Grouping Method



                  3             3       
315
                  9  

Step 1: 3 + 3 + 9 = 15 (1 set)


Step 2: 315 ÷ 15 = 21 sets


             21 sets of 15 mini cupcakes.


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


Step 3: 21 x 6 = 126


Step 4: 126 ÷ 3 = 42 (children)


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Children 2 units x  3  6 units
Adults 1 unit x  9 9 units
Total        15 units

 

Step 1: 15 units = 315

             1 unit = 315 ÷ 15

                       = 21 sets

Step 2: 2 units = 2 x 21

                        = 42 (children)



5)  

An angelfish costs $17. A goldfish costs $5 less than an angelfish. Sriram paid $539 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: $301


SOLUTION 1 :

 Grouping Method

                     $17  
$539
                        $12         $12         $12         $12      $12  

 

Step 1: $17 - $5 = $12 (goldfish)

Step 2: $12 + $12 + $12 + $12 + $12 + $17 = $77 (1 set)

Step 3: $539 ÷ $77 = 7 sets

              7 sets of $77 for fishes. 

              In each set, there are $60 for goldfishes.

Step 4: 7 x $60 = $420 (goldfish)

Step 5: 7 x $17 = $119 (angelfish)

Step 6: $420 - $119 = $301


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Goldfish 5 units x $12  60 units
Angelfish 1 unit x  $17 17 units 
Total        77 units

 

Step 1: 77 units = $539

             1 unit = $539 ÷ 77

                       = 7 sets

Step 2: 5 units = 5 x 7

                        = 35 

Step 3: 35 x $12 = $420 (goldfish)

Step 4: 7 x $17 = $119 (angelfish)

Step 5: $420 - $119 = $301



6)  

At a school funfair, every girl is given 2 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 432 packets of sweets were given out, how many girls were at the funfair 

Answer: 81


SOLUTION 1 :

 Grouping Method

               2             2           2  
432
             10  

Step 1: 2 + 2 + 2 + 10 = 16 (1 set)

Step 2: 432 ÷ 16 = 27 sets

             27 sets of 16 packets of sweets.

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

Step 3: 27 x 6 = 162

Step 4: 162 ÷ 2 = 81 (girls)


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Girls 3 units x  2  6 units
Boys 1 unit x  10 10 units
Total        16 units

 

Step 1: 16 units = 432

             1 unit = 432 ÷ 16

                       = 27 sets

Step 2: 3 units = 3 x 27

                        = 81 (girls)



7)  

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

Answer: 96


SOLUTION 1 :

 Grouping Method



                  5             5             5              5  
672
                 8  

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


Step 2: 672 ÷ 28 = 24 sets


             24 sets of 28 packets of chocolates.


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


Step 3: 24 x 20 = 480


Step 4: 480 ÷ 5 = 96 (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 = 672

             1 unit = 672 ÷ 28

                       = 24 sets

Step 2: 4 units = 4 x 24

                        = 96 (girls)



8)  

At a funfair, every child is given 5 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 608 mini cupcakes were given out, how many children were at the funfair 

Answer: 64


SOLUTION 1 :

 Grouping Method



                  5             5       
608
                  9  

Step 1: 5 + 5 + 9 = 19 (1 set)


Step 2: 608 ÷ 19 = 32 sets


             32 sets of 19 mini cupcakes.


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


Step 3: 32 x 10 = 320


Step 4: 320 ÷ 5 = 64 (children)


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Children 2 units x  5  10 units
Adults 1 unit x  9 9 units
Total        19 units

 

Step 1: 19 units = 608

             1 unit = 608 ÷ 19

                       = 32 sets

Step 2: 2 units = 2 x 32

                        = 64 (children)



9)  

An angelfish costs $11. A goldfish costs $6 less than an angelfish. Chidambaram paid $396 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

                     $11  
$396
                        $5         $5         $5         $5      $5  

 

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

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

Step 3: $396 ÷ $36 = 11 sets

              11 sets of $36 for fishes. 

              In each set, there are $25 for goldfishes.

Step 4: 11 x $25 = $275 (goldfish)

Step 5: 11 x $11 = $121 (angelfish)

Step 6: $275 - $121 = $154


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 = $396

             1 unit = $396 ÷ 36

                       = 11 sets

Step 2: 5 units = 5 x 11

                        = 55 

Step 3: 55 x $5 = $275 (goldfish)

Step 4: 11 x $11 = $121 (angelfish)

Step 5: $275 - $121 = $154



10)  

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 300 packets of sweets were given out, how many girls were at the funfair 

Answer: 45


SOLUTION 1 :

 Grouping Method

               3             3           3  
300
             11  

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

Step 2: 300 ÷ 20 = 15 sets

             15 sets of 20 packets of sweets.

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

Step 3: 15 x 9 = 135

Step 4: 135 ÷ 3 = 45 (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 = 300

             1 unit = 300 ÷ 20

                       = 15 sets

Step 2: 3 units = 3 x 15

                        = 45 (girls)