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 $17. A goldfish costs $3 less than an angelfish. Anand paid $435 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 3 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 378 packets of sweets were given out, how many girls were at the funfair 


Answer:_______________




3)  

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


Answer:_______________




4)  

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


Answer:_______________




5)  

An angelfish costs $13. A goldfish costs $6 less than an angelfish. Kumar paid $288 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 720 packets of sweets were given out, how many girls were at the funfair 


Answer:_______________




7)  

At a party, every girl is given 4 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 696 packets of chocolates were given out, how many girls were at the party 


Answer:_______________




8)  

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


Answer:_______________




9)  

An angelfish costs $15. A goldfish costs $5 less than an angelfish. Barathan 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:_______________




10)  

At a school funfair, every girl is given 4 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 378 packets of sweets were given out, how many girls were at the funfair 


Answer:_______________




 

1)  

An angelfish costs $17. A goldfish costs $3 less than an angelfish. Anand paid $435 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: $265


SOLUTION 1 :

 Grouping Method

                     $17  
$435
                        $14         $14         $14         $14      $14  

 

Step 1: $17 - $3 = $14 (goldfish)

Step 2: $14 + $14 + $14 + $14 + $14 + $17 = $87 (1 set)

Step 3: $435 ÷ $87 = 5 sets

              5 sets of $87 for fishes. 

              In each set, there are $70 for goldfishes.

Step 4: 5 x $70 = $350 (goldfish)

Step 5: 5 x $17 = $85 (angelfish)

Step 6: $350 - $85 = $265


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Goldfish 5 units x $14  70 units
Angelfish 1 unit x  $17 17 units 
Total        87 units

 

Step 1: 87 units = $435

             1 unit = $435 ÷ 87

                       = 5 sets

Step 2: 5 units = 5 x 5

                        = 25 

Step 3: 25 x $14 = $350 (goldfish)

Step 4: 5 x $17 = $85 (angelfish)

Step 5: $350 - $85 = $265



2)  

At a school funfair, every girl is given 3 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 378 packets of sweets were given out, how many girls were at the funfair 

Answer: 63


SOLUTION 1 :

 Grouping Method

               3             3           3  
378
             9  

Step 1: 3 + 3 + 3 + 9 = 18 (1 set)

Step 2: 378 ÷ 18 = 21 sets

             21 sets of 18 packets of sweets.

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

Step 3: 21 x 9 = 189

Step 4: 189 ÷ 3 = 63 (girls)


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Girls 3 units x  3  9 units
Boys 1 unit x  9 9 units
Total        18 units

 

Step 1: 18 units = 378

             1 unit = 378 ÷ 18

                       = 21 sets

Step 2: 3 units = 3 x 21

                        = 63 (girls)



3)  

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

Answer: 92


SOLUTION 1 :

 Grouping Method



                  2             2             2              2  
322
                 6  

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


Step 2: 322 ÷ 14 = 23 sets


             23 sets of 14 packets of chocolates.


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


Step 3: 23 x 8 = 184


Step 4: 184 ÷ 2 = 92 (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 = 322

             1 unit = 322 ÷ 14

                       = 23 sets

Step 2: 4 units = 4 x 23

                        = 92 (girls)



4)  

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

Answer: 50


SOLUTION 1 :

 Grouping Method



                  6             6       
525
                  9  

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


Step 2: 525 ÷ 21 = 25 sets


             25 sets of 21 mini cupcakes.


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


Step 3: 25 x 12 = 300


Step 4: 300 ÷ 6 = 50 (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 = 525

             1 unit = 525 ÷ 21

                       = 25 sets

Step 2: 2 units = 2 x 25

                        = 50 (children)



5)  

An angelfish costs $13. A goldfish costs $6 less than an angelfish. Kumar paid $288 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: $132


SOLUTION 1 :

 Grouping Method

                     $13  
$288
                        $7         $7         $7         $7      $7  

 

Step 1: $13 - $6 = $7 (goldfish)

Step 2: $7 + $7 + $7 + $7 + $7 + $13 = $48 (1 set)

Step 3: $288 ÷ $48 = 6 sets

              6 sets of $48 for fishes. 

              In each set, there are $35 for goldfishes.

Step 4: 6 x $35 = $210 (goldfish)

Step 5: 6 x $13 = $78 (angelfish)

Step 6: $210 - $78 = $132


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Goldfish 5 units x $7  35 units
Angelfish 1 unit x  $13 13 units 
Total        48 units

 

Step 1: 48 units = $288

             1 unit = $288 ÷ 48

                       = 6 sets

Step 2: 5 units = 5 x 6

                        = 30 

Step 3: 30 x $7 = $210 (goldfish)

Step 4: 6 x $13 = $78 (angelfish)

Step 5: $210 - $78 = $132



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

Answer: 135


SOLUTION 1 :

 Grouping Method

               2             2           2  
720
             10  

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

Step 2: 720 ÷ 16 = 45 sets

             45 sets of 16 packets of sweets.

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

Step 3: 45 x 6 = 270

Step 4: 270 ÷ 2 = 135 (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 = 720

             1 unit = 720 ÷ 16

                       = 45 sets

Step 2: 3 units = 3 x 45

                        = 135 (girls)



7)  

At a party, every girl is given 4 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 696 packets of chocolates were given out, how many girls were at the party 

Answer: 116


SOLUTION 1 :

 Grouping Method



                  4             4             4              4  
696
                 8  

Step 1: 4 + 4  + 4 ï»¿ + 4 + 8 = 24 (1 set)


Step 2: 696 ÷ 24 = 29 sets


             29 sets of 24 packets of chocolates.


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


Step 3: 29 x 16 = 464


Step 4: 464 ÷ 4 = 116 (girls)


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Girls 4 units x  4  16 units
Boys 1 unit x  8 8 units
Total        24 units

 

Step 1: 24 units = 696

             1 unit = 696 ÷ 24

                       = 29 sets

Step 2: 4 units = 4 x 29

                        = 116 (girls)



8)  

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

Answer: 68


SOLUTION 1 :

 Grouping Method



                  6             6       
714
                  9  

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


Step 2: 714 ÷ 21 = 34 sets


             34 sets of 21 mini cupcakes.


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


Step 3: 34 x 12 = 408


Step 4: 408 ÷ 6 = 68 (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 = 714

             1 unit = 714 ÷ 21

                       = 34 sets

Step 2: 2 units = 2 x 34

                        = 68 (children)



9)  

An angelfish costs $15. A goldfish costs $5 less than an angelfish. Barathan 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



10)  

At a school funfair, every girl is given 4 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 378 packets of sweets were given out, how many girls were at the funfair 

Answer: 54


SOLUTION 1 :

 Grouping Method

               4             4           4  
378
             9  

Step 1: 4 + 4 + 4 + 9 = 21 (1 set)

Step 2: 378 ÷ 21 = 18 sets

             18 sets of 21 packets of sweets.

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

Step 3: 18 x 12 = 216

Step 4: 216 ÷ 4 = 54 (girls)


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Girls 3 units x  4  12 units
Boys 1 unit x  9 9 units
Total        21 units

 

Step 1: 21 units = 378

             1 unit = 378 ÷ 21

                       = 18 sets

Step 2: 3 units = 3 x 18

                        = 54 (girls)