Do grouping.

Common multiple of 3 and 4 is 12
(3 x 4 = 12, 4 x 3 = 12)

Find the total cost of the same number of pens and pencils first.


Pencils : 3 for $2

So for 12 pencils, $2 x 4 = $8

Pens : 4 for $3

So for 12 pens, $3 x 3 = $9

Total cost of 12 pens and 12 pencils

= $8 + $9
= $17

Now group 12 pens and 12 pencils into 1 set.

With $51,

$51 ÷ $17 = 3

You can buy 3 sets.


Number of pencils bought
= 3 sets x 12 pencils per set
= 36 pencils

For part b) make the cost the same.

Common multiple for 3 and 2 is 6
(3 x 2 = 6, 2 x 3 = 6)

Pencils : 3 for $2

Now $2 x 3 = $6.
So for $6 , number of pencils

= 3 x 3
= 9


Pens : 4 for $3

Now $3 x 2 = $6.
So for $6, number of pens

= 4 x 2
= 8


9 - 8 = 1

For the same amount $6 each, you can 1 set of 9 pencils and 1 set of pens. You get 1 more pencil than pen.


So to get 10 more pencils than pens,

10 ÷ 1 = 10

You'll need 10 sets of 9 pencils and 10 sets of 8 pens.


Since each set of pencils and pens cost the same at $6,


Total cost
= total sets x price per set
= 20 x $6
= $120