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 $4 less than an angelfish. Prem paid $328 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 880 packets of sweets were given out, how many girls were at the funfair 


Answer:_______________




3)  

At a funfair, every child is given 2 mini cupcakes and every adult is given 10 mini cupcakes. There are twice as many children as adults who were at the funfair.

Given that a total of 476 mini cupcakes were given out, how many children were at the funfair 


Answer:_______________




4)  

At a party, every girl is given 3 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 399 packets of chocolates were given out, how many girls were at the party 


Answer:_______________




5)  

An angelfish costs $11. A goldfish costs $4 less than an angelfish. Kalai paid $460 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 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 400 packets of sweets were given out, how many girls were at the funfair 


Answer:_______________




7)  

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


Answer:_______________




8)  

At a party, every girl is given 2 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 450 packets of chocolates were given out, how many girls were at the party 


Answer:_______________




9)  

An angelfish costs $15. A goldfish costs $5 less than an angelfish. Raj paid $520 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 10 packets of sweets. There are thrice as many girls as boys who were at the funfair.

Given that a total of 484 packets of sweets were given out, how many girls were at the funfair 


Answer:_______________




 

1)  

An angelfish costs $17. A goldfish costs $4 less than an angelfish. Prem paid $328 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: $192


SOLUTION 1 :

 Grouping Method

                     $17  
$328
                        $13         $13         $13         $13      $13  

 

Step 1: $17 - $4 = $13 (goldfish)

Step 2: $13 + $13 + $13 + $13 + $13 + $17 = $82 (1 set)

Step 3: $328 ÷ $82 = 4 sets

              4 sets of $82 for fishes. 

              In each set, there are $65 for goldfishes.

Step 4: 4 x $65 = $260 (goldfish)

Step 5: 4 x $17 = $68 (angelfish)

Step 6: $260 - $68 = $192


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Goldfish 5 units x $13  65 units
Angelfish 1 unit x  $17 17 units 
Total        82 units

 

Step 1: 82 units = $328

             1 unit = $328 ÷ 82

                       = 4 sets

Step 2: 5 units = 5 x 4

                        = 20 

Step 3: 20 x $13 = $260 (goldfish)

Step 4: 4 x $17 = $68 (angelfish)

Step 5: $260 - $68 = $192



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

Answer: 120


SOLUTION 1 :

 Grouping Method

               4             4           4  
880
             10  

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

Step 2: 880 ÷ 22 = 40 sets

             40 sets of 22 packets of sweets.

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

Step 3: 40 x 12 = 480

Step 4: 480 ÷ 4 = 120 (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 = 880

             1 unit = 880 ÷ 22

                       = 40 sets

Step 2: 3 units = 3 x 40

                        = 120 (girls)



3)  

At a funfair, every child is given 2 mini cupcakes and every adult is given 10 mini cupcakes. There are twice as many children as adults who were at the funfair.

Given that a total of 476 mini cupcakes were given out, how many children were at the funfair 

Answer: 68


SOLUTION 1 :

 Grouping Method



                  2             2       
476
                  10  

Step 1: 2 + 2 + 10 = 14 (1 set)


Step 2: 476 ÷ 14 = 34 sets


             34 sets of 14 mini cupcakes.


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


Step 3: 34 x 4 = 136


Step 4: 136 ÷ 2 = 68 (children)


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Children 2 units x  2  4 units
Adults 1 unit x  10 10 units
Total        14 units

 

Step 1: 14 units = 476

             1 unit = 476 ÷ 14

                       = 34 sets

Step 2: 2 units = 2 x 34

                        = 68 (children)



4)  

At a party, every girl is given 3 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 399 packets of chocolates were given out, how many girls were at the party 

Answer: 84


SOLUTION 1 :

 Grouping Method



                  3             3             3              3  
399
                 7  

Step 1: 3 + 3  + 3 ï»¿ + 3 + 7 = 19 (1 set)


Step 2: 399 ÷ 19 = 21 sets


             21 sets of 19 packets of chocolates.


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


Step 3: 21 x 12 = 252


Step 4: 252 ÷ 3 = 84 (girls)


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Girls 4 units x  3  12 units
Boys 1 unit x  7 7 units
Total        19 units

 

Step 1: 19 units = 399

             1 unit = 399 ÷ 19

                       = 21 sets

Step 2: 4 units = 4 x 21

                        = 84 (girls)



5)  

An angelfish costs $11. A goldfish costs $4 less than an angelfish. Kalai paid $460 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: $240


SOLUTION 1 :

 Grouping Method

                     $11  
$460
                        $7         $7         $7         $7      $7  

 

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

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

Step 3: $460 ÷ $46 = 10 sets

              10 sets of $46 for fishes. 

              In each set, there are $35 for goldfishes.

Step 4: 10 x $35 = $350 (goldfish)

Step 5: 10 x $11 = $110 (angelfish)

Step 6: $350 - $110 = $240


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 = $460

             1 unit = $460 ÷ 46

                       = 10 sets

Step 2: 5 units = 5 x 10

                        = 50 

Step 3: 50 x $7 = $350 (goldfish)

Step 4: 10 x $11 = $110 (angelfish)

Step 5: $350 - $110 = $240



6)  

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

Answer: 48


SOLUTION 1 :

 Grouping Method

               5             5           5  
400
             10  

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

Step 2: 400 ÷ 25 = 16 sets

             16 sets of 25 packets of sweets.

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

Step 3: 16 x 15 = 240

Step 4: 240 ÷ 5 = 48 (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 = 400

             1 unit = 400 ÷ 25

                       = 16 sets

Step 2: 3 units = 3 x 16

                        = 48 (girls)



7)  

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

Answer: 60


SOLUTION 1 :

 Grouping Method



                  5             5       
570
                  9  

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


Step 2: 570 ÷ 19 = 30 sets


             30 sets of 19 mini cupcakes.


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


Step 3: 30 x 10 = 300


Step 4: 300 ÷ 5 = 60 (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 = 570

             1 unit = 570 ÷ 19

                       = 30 sets

Step 2: 2 units = 2 x 30

                        = 60 (children)



8)  

At a party, every girl is given 2 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 450 packets of chocolates were given out, how many girls were at the party 

Answer: 100


SOLUTION 1 :

 Grouping Method



                  2             2             2              2  
450
                 10  

Step 1: 2 + 2  + 2 ï»¿ + 2 + 10 = 18 (1 set)


Step 2: 450 ÷ 18 = 25 sets


             25 sets of 18 packets of chocolates.


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


Step 3: 25 x 8 = 200


Step 4: 200 ÷ 2 = 100 (girls)


SOLUTION 2 :

 Number x Value Method

 

  Number x Value Total Units
Girls 4 units x  2  8 units
Boys 1 unit x  10 10 units
Total        18 units

 

Step 1: 18 units = 450

             1 unit = 450 ÷ 18

                       = 25 sets

Step 2: 4 units = 4 x 25

                        = 100 (girls)



9)  

An angelfish costs $15. A goldfish costs $5 less than an angelfish. Raj paid $520 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: $280


SOLUTION 1 :

 Grouping Method

                     $15  
$520
                        $10         $10         $10         $10      $10  

 

Step 1: $15 - $5 = $10 (goldfish)

Step 2: $10 + $10 + $10 + $10 + $10 + $15 = $65 (1 set)

Step 3: $520 ÷ $65 = 8 sets

              8 sets of $65 for fishes. 

              In each set, there are $50 for goldfishes.

Step 4: 8 x $50 = $400 (goldfish)

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

Step 6: $400 - $120 = $280


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 = $520

             1 unit = $520 ÷ 65

                       = 8 sets

Step 2: 5 units = 5 x 8

                        = 40 

Step 3: 40 x $10 = $400 (goldfish)

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

Step 5: $400 - $120 = $280



10)  

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

Answer: 66


SOLUTION 1 :

 Grouping Method

               4             4           4  
484
             10  

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

Step 2: 484 ÷ 22 = 22 sets

             22 sets of 22 packets of sweets.

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

Step 3: 22 x 12 = 264

Step 4: 264 ÷ 4 = 66 (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 = 484

             1 unit = 484 ÷ 22

                       = 22 sets

Step 2: 3 units = 3 x 22

                        = 66 (girls)